Colloidal systems as experimental platforms for physics-informed machine learning

Abstract

Colloidal systems offer a unique experimental window for investigating condensed matter phenomena, uniquely enabling simultaneous access to microscopic particle dynamics and emergent macroscopic responses. Their particle-scale size, thermal motion, and tuneable interactions allow for real-time, real-space, and single-particle-resolved imaging. These features make it possible to directly connect local structural changes, dynamic rearrangements, and mechanical deformation with system-level behaviours. Such capabilities remain largely inaccessible in atomic or molecular systems. This review presents colloidal modelling as a predictive framework that addresses persistent challenges in materials research, including phase classification, dynamic arrest, and defect-mediated mechanics. We describe methodologies for extracting structural, dynamical, and mechanical descriptors from experimental imaging data, show how these features capture governing variables of material behaviour, and illustrate their application in machine learning approaches for phase identification, dynamics prediction, and inverse design. Rather than treating colloidal data as limited to model systems, we emphasize its value as a training ground for developing interpretable and physics-informed models. By linking microscopic mechanisms with macroscopic observables in a single experimental system, colloids generate structured and generalizable datasets. Their integration with data-driven methods offer a promising pathway toward predictive and transferable materials design strategies.

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Namhee Kang

Namhee Kang recently received a Master's degree from the Department of Chemical Engineering and Materials Science at Ewha Womans University. Her research focused on colloidal modeling of alloys, using particle-resolved experiments to explore structural disorder, phase transitions, and glass-forming ability. She is particularly interested in extracting governing descriptors from disordered materials for predictive modeling using colloidal systems as analogues for atomic materials.

Yeonseo Joo

Yeonseo Joo is currently pursuing a Master's degree in the Department of Chemical Engineering and Materials Science at Ewha Womans University. Her research focuses on colloidal cluster dynamics as a model platform probing crystallization, amorphous structure formation, and related processes in nature.

Hyosung An

Hyosung An is an Associate Professor in the Department of Petrochemical Materials Engineering at Chonnam National University. He earned his PhD in Chemical Engineering from Texas A&M University. His research focuses on polymers and composites, highlighting the use of electron tomography and three-dimensional quantitative analysis to reveal hidden structural rules in irregular morphologies, complemented by liquid AFM studies of nanoscale mechanics.

Hyerim Hwang

Hyerim Hwang is an Assistant Professor in the Department of Chemical Engineering and Materials Science at Ewha Womans University. She received her PhD in Applied Physics from Harvard University and her research spans colloidal materials from fundamental modeling to engineering applications, with a particular focus on data-driven approaches for understanding mechanisms. She works to establish colloidal systems as predictive experimental platforms for condensed matter and soft material phenomena.

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1. Introduction

Colloidal systems, composed of micrometre-scale particles (typically 200 nm to several micrometres in diameter for direct optical visualization) suspended in a fluid medium, have long served as experimental platforms for exploring the fundamental principles that govern condensed matter.¹ Their intermediate size allows them to undergo Brownian motion and exhibit tuneable interparticle interactions ranging from hard-sphere-like repulsion to electrostatic, depletion, or even DNA-mediated attraction, while remaining directly observable at the single-particle level.^2–4 With advanced optical techniques such as confocal, holographic, and differential dynamic imaging, we can track the particle trajectories, spatial configurations, and rearrangements of individual colloidal particles in three dimensions and over extended timescales. This direct visualization enables the study of otherwise inaccessible phenomena, including phase transitions, self-assembly dynamics, mechanical deformation, and glassy behaviour.^5–15

Beyond their imaging accessibility, colloidal systems offer unique tunability in terms of particle size, shape, interaction potential, and external responsiveness (Fig. 1(a)).^16–21 This versatility allows for systematic exploration of parameter space under controlled experimental conditions. For instance, poly(N-isopropylacrylamide) (NIPA) microgel spheres exhibit temperature-responsive swelling, allowing fine control over volume fraction and confinement geometry to induce phase transitions.^22,23 Similarly, sterically stabilized hard-sphere colloids can closely approximate idealized interparticle interactions, facilitating quantitative studies of crystallization, melting, and glass formation.² These model systems have proven invaluable for investigating the structure and dynamics of condensed matter in experimentally accessible yet theoretically tractable forms.

Fig. 1 Colloidal systems as experimental platforms linking microscopic structure to macroscopic behaviour. (a) Tuneable interparticle interactions in colloids, ranging from hard sphere to short range and long-range attractions, result in diverse phase behaviour under controlled conditions.²⁴ (b) Real space tracking provides simultaneous access to structure, dynamics, and mechanics, enabling the extraction of descriptors that govern macroscopic properties. These data flow into a complete machine learning pipeline, including data acquisition, feature extraction, physics-based modelling, and validation.

This experimental transparency has positioned colloids not only as analogues of atomic systems, but as magnifying platforms for uncovering the microscopic origins of macroscopic behaviour.²⁴ As illustrated in Fig. 1(b), real-space tracking provides simultaneous access to structure, dynamics, and mechanics, enabling the extraction of descriptors that directly govern macroscopic properties. Their ability to resolve structural and dynamical features such as local bond order, strain fields, dislocation networks, and nucleation precursors at single-particle precision, features that are rarely accessible in either atomic systems or coarse-grained simulations. This level of detail has transformed colloids from illustrative models to predictive testbeds for uncovering governing variables that dictate material behaviour across soft and out-of-equilibrium systems.

In parallel, the growth of data-driven approaches in materials research has elevated the importance of high-quality, structured datasets, particularly for machine learning (ML) applications.^25–30 While ML has demonstrated success in extracting hidden correlations and guiding materials discovery, its predictive power depends critically on the availability of structured, physically meaningful data.^31–36 For soft matter systems, conventional datasets derived from simulations often suffer from coarse-graining, idealized assumptions, or computational expense.^37–39 Colloidal systems offer a complementary solution to these challenges by serving as a high-fidelity platform for generating structured datasets with experimental grounding. Real-space colloidal data—ranging from particle coordinates and local order parameters to mechanical responses and temporal trajectories—can be systematically labelled, filtered, and augmented into descriptors suitable for ML pipelines. These data serve as inputs for supervised, unsupervised, and reinforcement learning models, linking microstructure to dynamics, mechanics, and emergent behaviours. Colloidal systems thus operate not only as models of matter but also as data refineries for ML-ready, physics-informed representations. This integration is schematized in Fig. 1(b), where descriptors obtained from real-space tracking flow into a physics-informed ML pipeline: from data acquisition and processing, to feature engineering and physics embedding, to model training and validation. This pipeline underscores how colloids serve as natural data engines, transforming particle-level observables into predictive frameworks.

Recent advances have illustrated how colloidal data can enrich ML capabilities in several domains, enabling the identification of structural motifs, the prediction of dynamic responses, and the optimization of self-assembly protocols.^16,40 Both supervised and unsupervised learning approaches have been applied to classify local environments and detect phase transitions.^41–46 Reinforcement learning has also begun to support adaptive control of self-assembly processes.^47–49 Notably, the most informative outcomes often arise when ML is integrated with experimentally curated datasets that reflect both structural fidelity and dynamic complexity.^50–52

This review examines colloidal modelling as a predictive framework for condensed matter and soft materials, with a particular emphasis on its integration with ML. Rather than positioning colloids in contrast to simulations, we emphasize their role as complementary tools, uniquely suited to produce interpretable, structured, and generalizable data for machine learning applications. We survey representative case studies in which colloidal systems have uncovered governing variables that are difficult to obtain by simulation alone. These examples are organized into three thematic areas: (1) structure, (2) dynamics, and (3) mechanics. Through these cases, we argue that colloidal systems are poised to become central contributors to physics-informed ML and the broader effort to build predictive, interpretable models of complex materials.

1.1. Machine learning fundamentals in materials science

Machine learning (ML) has rapidly become a central tool in materials science, chemistry, and physics, owing to its ability to uncover patterns in large and complex datasets. As its core, ML refers to algorithms that infer relationships between inputs and outputs directly from data, without being explicitly programmed with physical rules. In materials research, this often means mapping descriptors such as atomic configurations, scattering profiles, or thermodynamic quantities onto outcomes like phase identity, transport properties, or mechanical response.

Supervised learning has been the most widely adopted paradigm. In this approach, models are trained on labelled datasets to classify states (e.g., crystalline vs. amorphous phases) or to predict quantitative properties (e.g., diffusion coefficients).^53–57 Techniques range from linear regression and decision trees to more complex deep neural networks. Unsupervised learning, in contrast, does not rely on labels but instead identifies hidden structures through clustering or dimensionality reduction. Reinforcement learning, though less common in materials research, is increasingly applied to sequential decision-making tasks, such as designing synthesis pathways or controlling adaptive experiments.⁵⁸

These frameworks have already produced tangible advances. For example, supervised models have predicted alloy stability from compositional descriptors, learned formation energies of crystals from large density functional theory (DFT) datasets, and classified phases directly from diffraction patterns.^59–62 Unsupervised approaches have revealed hidden classes of glassy dynamics and clustered vast libraries of polymer structures without prior labels.^63,64 Reinforcement learning has been demonstrated for automating experimental design and guiding non-equilibrium process control.^58,65,66 Together, these cases illustrate how ML complements theory and simulation by accelerating discovery and revealing correlations that might otherwise remain hidden.

More comprehensive reviews of ML applications across materials science, chemistry, and physics covering topics such as high-throughput screening, autonomous laboratories, and generative models for materials design are available elsewhere.^67–69 In this review, we instead focus on how colloidal systems contribute uniquely to the development of physics-informed ML frameworks, offering experimentally accessible, high-fidelity datasets that link algorithmic methods with transparent and interpretable physical descriptors.

2. Real-space extraction of particle-level structure from optical imaging

The analysis of colloidal systems begins with high-dimensional, image-based observations that require careful processing to reveal physically meaningful features. While the colloidal size range spans from nanometres to micrometres, the experimental examples highlighted in this review, particularly those enabled by confocal microscopy, are typically limited to particles larger than ∼200 nm to ensure sufficient optical resolution for accurate particle localization. For particles below this optical resolution limit, where direct tracking is not feasible, complementary techniques such as scattering methods are required. Rather than relying solely on ensemble-averaged quantities, modern colloidal experiments generate time-resolved data that can be deconstructed into particle-resolved structural, dynamic, and mechanical descriptors. However, the first challenge lies in accurately resolving particle positions and linking them into coherent trajectories, particularly in dense, noisy, or low-contrast environments. Translating this experimental output into labelled and interpretable features is thus a foundational step for statistical analysis and machine learning workflows.

2.1. Experimental visualization of particle trajectories and configurations

Optical microscopy, particularly confocal microscopy, is a central to the quantitative study of colloidal systems (Fig. 2(a)). It enables single-particle resolution in three dimensions and direct visualization of local environments within dense suspensions.⁷⁰ Through time-resolved confocal imaging, researchers can track the motion, rearrangement, and interactions of particles over extended durations. This capability has been critical for studying phase transitions, glass formation, and stress relaxation in colloidal systems.^{14,15,23,71–81}

Fig. 2 Quantitative extraction of structural and mechanical descriptors from confocal microscopy and traction rheoscopy. (a) Schematic of the experimental setup of confocal microscopy.⁷⁰ (b) Representative single-particle coordinate data extracted from confocal image stacks. (c) 3-dimensional reconstruction of colloidal spheres from z-stacks, allowing identification of particle centres and local environments.⁷⁰ (d) Illustration of particle tracking and region-based exclusion for accurate dynamic analysis.⁸² (e) Application of traction rheoscopy to quantify spatially resolved strain. Left: Cross-sectional confocal image showing colloidal particles and fluorescent tracer particles embedded in the gel. Right: Height-resolved displacement data reveal strain localization near the colloidal–gel interface under shear deformation.⁸⁷

Particle localization from raw image stacks is typically accomplished using robust image analysis algorithms. One widely adopted method is the approach developed by Gao and Kilfoil,⁸² which combines bandpass filtering and centroid fitting to achieve sub-pixel accurate localization, even in dense and noisy samples (Fig. 2(b)). In more complex experimental contexts, this base routine is augmented with image deconvolution, nonlinear least-squares fitting, and pixel-wise neural network classification. These additional steps enhance the accuracy of particle identification, particularly for distinguishing monodisperse particles from synthesis by-products such as dimers or aggregates (Fig. 2(c)).

Once particles are localized, their trajectories are constructed across frames using distance-based association algorithms.^83,84 In dilute systems, where particle displacements are moderate and isolated, classical tracking methods such as Crocker–Grier algorithm, widely implemented in Trackpy, perform reliably by minimizing frame-to-frame displacement. However, challenges arise in dense suspensions, especially those near glass or jamming transitions, where particle displacements vary broadly and neighbouring particles are in close proximity. In such systems, a single cutoff distance for trajectory is inadequate, as small displacement risk exclusion under a large cutoff, while large displacements introduce ambiguity under a small one. As shown in Fig. 2(d), a two-pass tracking strategy addresses this challenge by applying a small cutoff in the first pass to accurately capture low-displacement particles. After removing these from the dataset, the second pass uses a larger cutoff to recover particles undergoing larger displacements. This hierarchical approach resolves a wide range of mobilities while minimizing misidentification. These capabilities are essential for extracting meaningful dynamical quantities such as mean square displacement (MSD), cage rearrangements, and collective flow patterns, particularly in systems exhibiting strong dynamic heterogeneity.

To support large-scale, reproducible analysis, high-throughput pipelines built using open-source tools such as DeconvolutionLab2, TrackMate, TrackPy, and Colloidoscope have recently become standard.^83,85,86 For example, TrackPy enables flexible control over linking parameters and supports custom tracking strategies, while Colloidoscope offers deep-learning-enhanced detection for dense, noisy datasets. These tools enable automated particle localization and trajectory reconstruction across large 3D datasets, facilitating consistent feature extraction for downstream structural, dynamic, and mechanical analyses.

A recent advancement in experimental methodology, traction rheoscopy, has enabled direct mechanical characterization of colloidal materials at both the macroscopic and single-particle level (Fig. 2(e)). This technique combines confocal imaging with a compliant, calibrated elastic substrate to simultaneously measure shear stress and internal strain.⁸⁷ The substrate's deformation is tracked via embedded fluorescent markers, yielding millipascal-level stress resolution, while particle tracking within the colloid provides displacement fields from which local strain tensors can be computed. Using best-fit affine transformations, strain is decomposed into shear, dilation, and rotation components, enabling detailed mapping of stress evolution under load. For example, 1 μm lateral displacement at the surface of a 143 μm-thick silicone gel (G ≈ 4.9 Pa) corresponds to a shear stress of ∼ 34 mPa. Importantly, this approach resolves stresses below 1 mPa and captures spatial stress heterogeneities throughout the colloidal domain, offering rare experimental access to the internal force landscape during deformation.

2.2. Quantitative feature extraction from particle-resolved data

Once particle coordinates and trajectories have been reconstructed, they form the foundation for extracting a wide range of physical descriptors including structural order, mobility, and internal stress at the single-particle level. These features, which will be discussed in Section 3, enable researchers to identify crystalline symmetries, map dynamic heterogeneity, and quantify mechanical response under deformation. This transformation from image to data-rich representation is central to modern colloidal science and provides a robust framework for data-driven modelling and machine learning.

3. Governing descriptors from colloidal experiments

Building on the real-space extraction techniques discussed in the previous section, this section organizes the key microscopic descriptors that can be directly measured from colloidal experiments and are used to characterize complex material behaviour. These descriptors are not merely computational constructs; they arise from optical tracking of particle configurations and motions, enabling precise and interpretable insight into the structural organization, dynamic evolution, and mechanical response of colloidal systems. The subsections are arranged according to descriptor type: structural, dynamic, and mechanical. By systematically categorizing these observables, we emphasize how colloidal platforms serve as powerful experimental testbeds for identifying governing variables, such as local order, mobility, and stress, that are essential for understanding phase transitions, mechanical yielding, and glassy dynamics in soft matter. Here we highlight a representative subset of commonly used descriptors in each category; a broader perspective on emerging and future directions is provided in the concluding remarks of this section.

3.1. Structural descriptors

Structural descriptors provide a quantitative basis for identifying and classifying local particle arrangements in colloidal systems. These metrics condense the high-dimensional geometric configuration of neighbouring particles into scalar or vector quantities that are sensitive to symmetry, density, or packing, or entropy. They allow for precise identification of phases, and amorphous regions and are commonly used in phase transition studies and as input features for machine learning models.

A widely used family of structural metrics is the bond-orientational order parameter q_l and their rotational invariant w_l, originally developed by Steinhardt, Nelson, and Ronchetti to identify local symmetries in atomic systems and later adapted for colloidal suspensions.⁸⁸ Among these, q₆ quantifies six-fold symmetry and is commonly used to distinguish between crystalline and liquid-like environment; high q₆ values typically correspond to ordered states such as face-centred cubic (FCC), hexagonal closed packed (HCP), or body-centred cubic (BCC), while lower values indicate disorder (Fig. 3(a)).⁸⁹ The third-order invariant w₆ provides finer differentiation between polymorphs such as FCC and HCP (Fig. 3(b)).⁹⁰ These harmonic-based descriptors are widely employed to classify crystalline motifs during nucleation and growth.

Fig. 3 Structural descriptors extracted from colloidal experiments. (a) Distribution of Steinhardt bond-order parameters (q₄, q₆, w₆) used to distinguish local crystal symmetries such as face-centred cubic (fcc), body-centred cubic (bcc), hexagonal close-packed (hcp), and icosahedral structures in particle-resolved colloidal data.⁸⁹ (b) Visualization of crystalline domains identified by bond-order parameters, enabling the mapping of spatial heterogeneity in nucleating systems.⁹⁰ (c) Time-resolved tracking of crystal growth dynamics using local order parameters and number of crystal neighbours, with particle configurations reconstructed in real space from confocal imaging.⁸ (d) Detection of discontinuous solid–solid transitions in a binary colloidal monolayer driven by magnetic fields.⁹²

In more specific experimental contexts, empirical metrics tailored to the system's geometry provide practical alternatives. For example, in studies of BCC colloidal crystallization and melting, an in-line bond angle order parameter ψ_i, defined as the number of neighbour pairs with bond angles within 180°, is used to distinguish crystalline from liquid particles. A threshold value of ψ_i > 3.5 effectively identifies ordered regions, while additional classification by the number of crystalline neighbours Z enables resolution of bulk, interfacial, and liquid phases with single-particle precision, allowing dynamic tracking of melting fronts and interface evolution (Fig. 3(c)).^8,91 In another example, Alert et al. employed the lattice angle α as an order parameter in a two-dimension (2D) dipolar colloidal crystal, where a discontinuous change in α under varying magnetic field strength signalled a mixed-order phase transition.⁹²

While traditional and empirically tuned order parameters are effective in classifying local structures into crystalline, hexatic, or amorphous states, more sophisticated descriptors offer deeper insight into structure–property relationships.^8,88,91 In addition to these traditional metrics, we discuss a representative selection of higher-level governing descriptors that have been developed that extract deeper thermodynamic or dynamic information from particle-resolved experimental data (Fig. 4). These descriptors have proven powerful in identifying phase transitions and structural heterogeneities.

Fig. 4 Structural descriptors capturing spatial heterogeneity and anisotropy in colloidal glasses. (a) Anisotropy parameter k derived from Voronoi cell shape analysis distinguishes between isotropic and anisotropic packing in colloidal systems. The onset of glassy dynamics coincides with a transition from anisotropic to isotropic local environments.⁹⁴ (b) Depth-resolved maps of local density ρ and Debye–Waller factor (DW) reveal the formation of a surface mobile layer in binary colloidal glasses. Structural relaxation is suppressed toward the interior, where glassy arrest dominates.⁹⁵ (c) Local entropy s₂ identifies nucleated dense phases in supercooled colloidal vapors. Snapshots at varying undercooling show the emergence and growth of clusters, with 3D reconstructions highlighting local order.⁹⁸

One such descriptor is the Voronoi anisotropy parameter k = |R_min|/|R_max|, shown in Fig. 4(a), which quantifies the elongation of particle's local cage based on the geometry of its Voronoi cell.^93,94 A value of k ≈ 1 indicates a highly isotropic cage, while lower k values reflect anisotropic, elongated cages. As shown in Fig. 4, the averaged anisotropy k increases with packing fraction ϕ, capturing the isotropization of cages as systems approach the glass transition. This behaviour was observed in simulations of monodisperse hard-sphere and soft Weeks–Chandler–Andersen (WCA) particles in 2D and 3D, where softer particles form more isotropic cages due to their greater configurational flexibility. These trends were experimentally validated using binary colloidal monolayers of soft poly(N-isopropylacrylamide) (NIPA) and hard poly(methyl methacrylate) (PMMA) particles reproduced the behaviour of 2D WCA and hard-sphere systems, respectively.⁹⁴ Because k correlates with dynamical heterogeneity, it serves as a predictive structural marker for glassy behaviour; Fig. 4(b) overlays the k with the Debye–Waller factor, a dynamic descriptor that reflects particle vibrational amplitude.

Another descriptor is the local two-body excess entropy s₂ and local density ρ, which provide thermodynamic insights into the degree of structural order around each particle.^95,96 The local density ρ_i = πσ_i²/(4A_i), defined as the inverse area of a particle's Voronoi cell, captures the degree of local packing, while s_2,i, computed from local pair correlation functions, quantifies the loss of configurational entropy due to structural correlations.⁹⁷ Lower s₂ values correspond to well-packed, ordered environments, while higher values indicate more disordered, fluid-like regions. As illustrated in Fig. 4(b), these descriptors ρ(y) and s₂(y) show that surface pre-melting in a binary colloidal monolayer under slow cooling occurs gradually rather than abruptly. Instead of a sharp interface, a sequence of distinct layers emerges: a dense vapor, a surface liquid, a dynamically arrested surface glassy layer, and finally the bulk glass. The interface positions y₀, y₁, y₂ are defined by the saturation of normalized ρ and s₂, highlighting how these descriptors capture subtle transitions across the interface. These descriptors are highly sensitive to subtle changes in structural order and are widely used in studies of vitrification and confinement effects.

A simpler yet effective geometric descriptor is the local coordination number, defined as the number of neighbouring particles within a specified radial cut-off. As shown in Fig. 4(c), this metric was used to distinguish gas, liquid, and solid phases in a colloidal system undergoing phase transitions induced by critical Casimir forces.⁹⁸ Confocal imaging captured a gradual evolution from a low-density gas phase to high-density liquid clusters and crystalline domains as the temperature approached the critical point. Particles with higher coordination numbers were identified as belonging to denser, more structured regions, while low-coordination particles reflected gas-like surroundings. This simple neighbour-counting method allows for real-time, particle-resolved phase classification based on local density fluctuations and remains highly compatible with optical microscopy-based colloidal experiments.

Together, these descriptors from bond-orientational harmonics to entropy metrics and coordination-based order parameters translate raw positional data into a robust, interpretable structural language. They not only support real-time classification of condensed matter states but also serve as foundational inputs for machine learning models predicting particle mobility, yielding, and self-assembly pathways.

3.2. Dynamic descriptors

Dynamic descriptors capture the time-dependent behaviour of particles and are essential for characterizing mobility, dynamic heterogeneity, and relaxation processes in colloidal systems;^6,99,100 they arise from approaches that track particle motion over time, using displacement statistics, time-correlation functions, or higher-order fluctuation analyses. Widely used examples include the mean squared displacement (MSD), the van Hove self- and distinct correlation functions, the self-intermediate scattering function, dynamic susceptibilities, structural relaxation times, and mobility-based indicators. Here, we discuss representative key examples, including MSD, the self-intermediate scattering function, and the Lindemann parameter, which are widely adopted for characterizing mobility and structural instability. These metrics are typically extracted from particle trajectories and provide insight into both short-time vibrations and long-time rearrangements, which are critical for understanding the transition from fluid-like to arrested states such as glasses or crystals.

Mean square displacement (MSD) is a fundamental dynamic descriptor that measures the average squared displacement of particles over time.¹⁰¹ It is defined as:

MSD(t) = 〈Δr²(t)〉 = 〈[r_i(t₀ + t) − r_i(t)]²〉

Fig. 5(a) illustrates how MSD is experimentally measured using real-time tracking of colloidal particles.^102,103 Sequential imaging captures particle positions at high frame rates, while trajectory maps show Brownian motion over time. From this image sequence, MSD is computed as the squared displacement between positions separated by a time lag t, averaged over many particles. The resulting MSD vs. time plot confirms the linear scaling expected for free diffusion, while velocity fluctuation analysis reveals the stochastic nature of thermal motion.⁸ MSD reveals distinct dynamic regimes: it grows linearly in dilute fluids (free diffusion), saturates in crystals due to confinement within lattice cages, and exhibits a two-step pattern in glassy or supercooled states. These behaviours are clearly visualized in Fig. 5(b), which shows ensemble-averaged MSDs at various volume fractions. As ϕ increases, the overall MSD decreases, and the characteristic relaxation time is delayed. The initial plateau in the MSD curve reflects cage trapping, and the end of the plateau, where the MSD resumes growing marks the onset of cage rearrangements.

Fig. 5 Dynamic descriptors capturing particle mobility, relaxation, and nucleation. (a) Particle trajectories, mean-square displacement (MSD), and velocity profiles extracted from confocal time-series illustrate translational dynamics in dense colloidal systems.¹⁰³ (b) MSD scaling as a function of volume fraction reveals the onset of dynamical arrest, consistent with glass-like behaviour.⁶ (c) Self-intermediate scattering function F_s(q,t) for all particles across a series of temperatures in glass-forming liquids, illustrating the two-step relaxation typical of glass-forming systems.¹⁰⁹ (d) Maps of the dynamic Lindemann parameter quantify spatially resolved fluctuations, allowing the detection of soft regions prior to crystallization.¹⁰ (e) and (f) Time-resolved mapping of local displacement fields identifies dynamic heterogeneity and nucleation events.^111,112

Another widely used dynamic descriptor is the self-intermediate scattering function (ISF), F_s(q,t).¹⁰⁴ It quantifies temporal correlations in particle positions at a given wavevector q. The ISF is defined as:

where N is the number of particles, q is the wavevector, r_j(t) is the position of particle j at time t, and 〈 〉 denotes an ensemble average.¹⁰⁴ Experimentally, the ISF can be obtained from dynamic light scattering or X-ray photon correlation spectroscopy, and in colloidal systems it is widely used to detect vitrification.^105–108 In glass-forming colloids, F_s(q,t) exhibits a characteristic two-step decay: an initial relaxation due to local vibrations within cages formed by neighbouring particles, and intermediate-time plateau where particles remain trapped and the system becomes dynamically arrested, and finally a slow relaxation as collective cage rearrangements allow particles to escape their local minima and the F_s(q,t) decays to zero. The α-relaxation time τ_α is conventionally defined as the time required for F_s(q,t) to decay to 1/e. This behaviour is illustrated in Fig. 5(c), where the emergence of the plateau and delayed α-relaxation clearly marks the transition from fluid-like to glassy dynamics.¹⁰⁹

Closely related to the MSD, the Lindemann parameter provides a local criterion for detecting melting and structural instability by quantifying relative vibrational amplitudes between neighbouring particles.¹¹⁰ It is defined as:

where Δr_j(t) and Δr_k(t) are the displacements of neighbouring particles j and k from their equilibrium positions, and a is the mean lattice spacing.¹¹⁰ As shown in Fig. 5(d)–(f), this metric has been employed across a range of contexts to pinpoint local disorder and incipient phase transitions.^10,111,112 In thermally driven melting (Fig. 5(d)), superheating leads to elevated vibrational amplitudes in the crystal interior, with high L values identifying sites of liquid nucleation within an otherwise ordered lattice. At crystal–liquid interfaces (Fig. 5(e)), particles exceeding the Lindemann threshold (typically, L ∼ 0.1–0.18) signal localized instability preceding homogeneous melting. In shear-driven systems (Fig. 5(f)), boundary-induced rearrangements can raise L beyond the melting threshold even in the absence of thermal excitation, triggering plastic events or virtual melting. Notably, the Lindemann parameter saturates rapidly (∼1 s) in colloidal systems, enabling real-time monitoring of structural fluctuations. Its near-universal threshold and local sensitivity make it a powerful tool for tracking dynamic instabilities at interfaces, grain boundaries, and defect-rich regions in soft crystalline materials.

3.3. Mechanical descriptors

Mechanical descriptors quantify how materials respond to applied forces and deformations, capturing key properties like elasticity, plasticity, and strength. They are derived from approaches that measure or reconstruct how materials deform and transmit stress under external or thermal forces. In colloidal systems, these responses can be resolved at the single-particle level due to their micro-meter scale of the particles, their slow Brownian motion, and the compatibility of these systems with high-resolution imaging. Unlike structural or dynamic metrics, mechanical metrics provide direct insight into how materials bear stress, redistribute force, and ultimately yield or fail.

Recent advances in techniques like traction rheoscopy and confocal microscopy have made it possible to map local stress and strain fields with particle-level precision, offering an unparalleled view into the mechanics of soft matter systems under mechanical load.^{6,87,113–117} Using these methods, a range of key descriptors can be directly extracted from particle-resolved data, offering complementary perspectives on deformation, stress transmission, and bulk stability.^115,118 Osmotic pressure can is an important descriptor of the mechanical properties of colloidal dispersions, as it reflects how interparticle interactions and thermal motion define the system's equation of state.¹¹⁹ It can be reconstructed from particle-level data across many particles, for example by averaging local forces or structural correlations, thereby linking microscopic observables to bulk behaviour.^120,121 In this review, however, we focus primarily on particle-resolved descriptors, since they provide direct microscopic insight into local deformation and stress. Here, we highlight representative examples, including the strain tensor, von Mises strain, and reconstructed stress, that have proven particularly powerful in revealing plastic flow, dislocation activity, and defect-mediated mechanics in colloidal systems.

Strain (γ or ε) is a fundamental mechanical descriptor that measures material deformation through relative particle displacements of neighbouring particles.^87,122 In colloidal systems, strain can be computed with single-particle resolution by tracking individual displacements. The local strain tensor is calculated from changes in a particle's nearest-neighbour distances, capturing local shear deformation.

A pioneering study by Schall et al. demonstrates that the thermally or externally-driven strain fields can be resolved at single-particle resolution in colloidal glasses.¹¹⁵ By tracking particle trajectories in dense colloidal suspensions and computing local strain tensors from particle displacements, they identified how structural arrangements arise and evolve under shear. As shown in Fig. 6(a), the cumulative shear strain ε_yz was mapped over time during continuous shear, revealing localised regions of elevated strain (shear transformation zones) progressively coalesce into a system-spanning network. These zones emerge intermittently and spatially heterogeneously, suggesting the discrete nature of plastic events in amorphous solids.

Fig. 6 Mechanical descriptors extracted from particle-resolved deformation in colloidal crystals. (a) Time evolution of local shear strain during deformation. Top: 2D strain maps (ε_yz component) reveal spatially heterogeneous transformation zones at 20, 30, and 50 minutes of applied shear. Bottom: 3D renderings highlight particles exceeding a critical shear strain threshold, showing the progressive formation of strain-localized networks.¹¹⁵ (b) Colormap of cumulative strain from 3D tracking in a sheared colloidal crystal, revealing regions of persistent defor-mation.⁸⁷ (c) von Mises strain maps capturing equivalent shear deformation. Plastic flow is visualized through slip along both classical [111] and unconventional [001] planes, revealing complex strain propagation paths under external loading.¹²³

One scalar form used to analyse the particle-level deformation is the von Mises strain ( ), which quantifies local distortion strain and is particularly useful for detecting slip events and zones of strain localization.⁸⁷ It is defined as:

ε_vM = [ε_xy² + ε_xz² + ε_yz² + 1/6((ε_xx − ε_yy)² + (ε_yy − ε_zz)² + (ε_zz − ε_xx)²)]^1/2.

By computing the root mean square variation of ε_vM across time and space, one can visualise the temporal evolution and spatial heterogeneity of shear response within the colloidal solid (Fig. 6(b)). For instance, when a hard-sphere colloidal glass is deformed under shear, traction rheoscopy reveals grid-like patterns of elevated shear strain near embedded metal meshes, highlighting regions where plastic deformation is concentrated.

A recent study reveals particle-resolved mechanical behaviour by directly measuring ε_vM at single-particle resolution during shear deformation of hard-sphere colloidal crystals.¹²³ As shown in Fig. 6(c), this approach enabled them to capture the onset and evolution of plastic flow; at total strain γ ≈ 0.04, elevated ε_vM values appear along [111] slip planes, consistent with classical dislocation glide, and at γ ≈ 0.06, strain becomes more localized and activates additional slip along unconventional (001) planes. These spatially resolved strain fields, correlated with dislocation structures and local rearrangements, revealed that colloidal crystals exhibit Taylor-like work hardening despite their entropic elasticity.^124–126

While strain captures how a material deforms, stress (σ) quantifies the internal forces that drive such deformation, typically expressed as force per unit area. In soft materials like colloidal assemblies, shear stress (σ_xz) is particularly relevant under external loading. Recent developments such as traction rheoscopy (Fig. 2(e)) have enabled direct, spatially resolved stress measurements in colloidal solids with millipascal sensitivity.⁸⁷ These approaches extend beyond global stress–strain characterization to reveal how internal stresses vary across space, time, and microstructure.

Defect-level stress mapping in Fig. 7(a) has revealed how stress concentrates locally around microscopic imperfections.¹¹⁸ In a colloidal crystal with a single vacancy, Lin et al. used SALSA (stress assessment from local structural anisotropy) to reconstruct local stress tensors from confocal microscopy data (Fig. 7(a)). This method estimates the stress by integrating directional correlations in the local pair distribution function g(r), assuming hard-sphere-like interactions. They found that the stress field around the vacancy decays gradually over several particle diameters and exhibits a dipole-like shear stress pattern, consistent with predictions from continuum elasticity. Although the modulus remains nearly uniform, the vacancy induces significant local stress anisotropy and long-range distortion of the surrounding stress field. This highlights the utility of colloidal systems for directly visualising stress transmission around point defects. The same approach has been applied to visualise stress fields around extended crystalline defects such as dislocations and grain boundaries, as shown in Fig. 7(b) and (c). In Fig. 7(b), the local shear stress surrounding an edge dislocation in a two-dimensional colloidal crystal exhibits a quadrupolar symmetry, closely matching predictions from linear elasticity.¹²⁷ Fig. 7(c) shows stress distributions in a polycrystalline monolayer, where strong heterogeneity in shear and pressure fields emerges near grain boundaries and triple junctions. These measurements reveal how stress localizes along misoriented domains and evolves dynamically as grains rearrange. These examples demonstrate the capability of colloidal systems to directly test continuum elasticity at the particle scale and to capture the complex, collective mechanics of defect networks in soft crystals.

Fig. 7 Stress and modulus mapping around crystal defects in colloidal solids. (a) Particle-resolved stress field in a 3D colloidal crystal containing a single vacancy. The SALSA method reconstructs the local stress tensor from confocal microscopy data, revealing dipolar shear stress patterns and long-range stress distortion consistent with continuum elasticity predictions.¹¹⁸ (b) Local stress analysis around an edge dislocation and associated stacking fault. The quadrupolar shear stress field surrounding the dislocation, extracted from both experiment and simulation, closely matches theoretical expectations. The shear modulus G decreases near the dislocation core, as shown by position-dependent modulus mapping.¹¹⁸ (c) Stress distributions in a polycrystalline colloidal monolayer. SALSA analysis captures spatial heterogeneity in pressure and shear stress, particularly at grain boundaries and triple junctions, highlighting localized stress concentrations and collective mechanical behaviour in defect-rich soft crystals.¹¹⁸

While the focus in this section has been on established and widely used descriptors, it is equally important to consider how new descriptors may emerge to address current limitations. Although the literature contains many specialized variants tailored to particular systems, most can be understood as tuned parameters or extensions of the fundamental quantities discussed here. The rapid progress of particle-resolved imaging and analysis ensures that this list will continue to grow. In particular, the integration of high-fidelity experimental datasets with ML is expected to accelerate the development of new, physics-informed descriptors that extend beyond traditional human-designed metrics. Such advances may uncover hidden order parameters, detect precursor dynamics in glassy or crystallizing states, and link microscopic stress transmission directly to macroscopic response.

4. Predictive modelling from simulated colloidal data

The successful application of ML to colloidal systems relies not only on algorithmic sophistication but critically on the availability of well-structured and physically grounded input data. Colloidal experiments uniquely generate real space data that capture structural, dynamical, and mechanical features across both microscopic and macroscopic scales. This multiscale observability enables the extraction of rich descriptors that can be effectively reshaped into ML inputs capable of producing accurate predictions.^16,128 In this context, we define predictive modelling as the data-driven inference of phase, dynamics, or interaction parameters based on features extracted from colloidal experimental data. This includes classifying structural states, forecasting dynamic evolution, and designing interaction potentials that yield desired assembly outcomes. The following subsections outline how predictive frameworks based on ML have been used to overcome long-standing challenges in colloidal modelling, including: (1) classifying structural states in complex or disordered phases where conventional order parameters fail, (2) forecasting dynamic evolution and discovering hidden kinetic pathways, and (3) solving the inverse problem of designing new materials with targeted properties.

4.1. Structure-to-phase classification

Traditional methods for classifying colloidal self-assembly states often rely on order parameters, which are aggregate variables defined through physics reasoning; examples include the order parameters (e.g., q₄, q₆) used to distinguish crystalline symmetries, the radial distribution function g(r) to probe positional order, etc. While effective in simple or ideal systems, such descriptors are often limited in their ability to distinguish multicomponent, anisotropic, or partially ordered phases, where no single parameter cleanly separates states.

ML mitigates these limitations by leveraging the wide range of descriptors available from colloidal experiments. Instead of relying solely on scalar metrics, full particle configurations such as neighbour distances, angular distributions, and Voronoi volumes, can be used to detect subtle correlations and higher order motifs that elude traditional descriptors. This makes ML based classification especially valuable for identifying glassy, polycrystalline, or hierarchically structured phases.^{54,57,64,129,130}

A prominent example is the use of convolutional neural networks (CNNs) for image based classification.¹³¹ These networks can be trained to recognize different self-assembled structures, including crystals, liquid crystals, and quasicrystals, directly from diffraction patterns or microscopy images without needing predefined descriptors (Fig. 8(a)). Input images may be rotated or rescaled to improve robustness during training, allowing CNNs to generalize across various orientations and experimental conditions. In parallel, unsupervised learning techniques, such as clustering based on pixel-level features or autoencoder representations, have been used to sort unlabelled images into physically meaningful groups.⁴⁶ This approach can uncover subtle distinctions such as void-rich defective states versus fully ordered crystals that are often missed by conventional bond-orientational order parameters. Once the unsupervised clusters are interpreted and assigned to meaningful structural labels, the resulting annotations can be used to train supervised CNNs. These models can then rapidly and accurately classify new structures without requiring manually tuning or handcrafted features, enabling high-throughput analysis across diverse assembly conditions.^57,132,133

Fig. 8 Machine learning-based structural classification and nucleation pathway analysis of colloidal assemblies. (a) Schematic workflow of image-based classification using convolutional neural networks (CNNs).¹²⁸ (b) Structure classification in binary colloidal superlattices (BSLs) using graphlet-based deep autoencoders. Local neighbourhoods are encoded as structural and compositional graphs via branched graphlet decomposition, which are then compressed into low-dimensional latent spaces using autoencoders.¹³⁴

For more complex systems (Fig. 8(b)), particularly in three dimensions, deep autoencoders have been integrated with neighbourhood graph frameworks to handle structural and compositional order.¹³⁴ Branched graphlet decomposition maps the local environment of each particle onto high-dimensional graphs that encode geometry and particle identity. These graph representations are then compressed into lower-dimensional latent spaces using deep autoencoders, which preserve essential features while filtering out redundancies. This method has proven especially effective for classifying binary colloidal superlattices, distinguishing ideal crystal structures such as FCC-CuAu or BCC-CsCl, as well as irregular configurations including substantial defects and intermediate states. The graphlets serve as the primary structural descriptors in this framework, simultaneously capturing local symmetry, bonding motifs, and species-specific arrangements. By embedding both spatial and compositional information, this strategy enables a detailed, particle-level view of nucleation pathways and ordering transitions, making it particularly powerful for complex or multicomponent colloidal systems.

4.2. Dynamics and kinetics

Classical measurements such as calorimetry or diffraction provide ensemble-averaged information, which often lacks the spatiotemporal resolution required to track microscopic kinetics or transient structural motifs.¹⁰ Even with simulation-based modelling, it remains difficult to extract interpretable dynamical variables that faithfully describe evolving particle systems. Colloidal systems, with tuneable interactions and particle-resolved trajectories, provide a rich testbed for investigating these kinetic pathways. Yet, quantifying the evolution of structure and motion across many particles and time frames requires tools that can learn from complex, high-dimensional data. ML enables this by uncovering latent patterns in trajectories, predicting dynamic rearrangements, and identifying relevant timescales, without relying on pre-defined assumptions.

A major approach involves predicting long-term behaviour from short-time structural descriptors. For instance, supervised models trained on local particle configurations represented through radial and angular distributions, Voronoi geometry, or local entropy can predict which particles will undergo rearrangement.⁹⁴ These descriptors are reshaped into feature vectors and used to train classifiers or regressors that forecast future mobility.⁵⁴ Such models reveal correlations between structure and dynamics, providing access to hidden soft spots and indicators of dynamic heterogeneity.

A significant advance in this direction is the development of machine-learned collective variables (CVs) that guide simulations of phase transitions, as shown in Fig. 9(a).¹³⁵ Recent work uses graph neural networks (GNNs) trained on particle neighbourhoods to efficiently learn CVs like local coordination or Steinhardt bond-order.^136,137 These models bypass the need for manual descriptor selection and offer orders-of-magnitude faster computation during enhanced sampling, enabling efficient exploration of rare events like crystallization or spinodal decomposition. Remarkably, GNNs trained on colloidal systems have been successfully transferred to simulate metallic nucleation (e.g., copper), highlighting their cross-domain generalizability.

Fig. 9 Graph neural network (GNN)-based learning of nucleation pathways. (a) A GNN framework transforms particle coordinates into latent representations through neighbour-based graph construction, edge embedding, and pooling, enabling prediction of nucleation collective variables.¹³⁵ (b) Application to binary colloidal superlattices reveals a classical one-step nucleation pathway via compositionally ordered (CO) clusters, contrasting the two-step route in Fig. 8.¹³⁴

ML also supports the discovery of self-assembly pathways that defy conventional intuition (Fig. 9(b)). Using unsupervised learning applied to simulated trajectories, researchers have reconstructed phase transition landscapes and uncovered nonclassical nucleation routes.¹³⁴ For example, in binary colloidal mixtures, graph-based latent embeddings revealed that superlattice formation often proceeds via dense amorphous precursors rather than direct crystallization. This capability to detect hidden intermediates and precursor states, especially in systems exhibiting frustration or metastability, is not easily achievable through conventional trajectory averaging.

4.3. Inverse design of assembly

Classical colloidal research has largely focused on “forward design” which starts from known particle attributes (e.g., size, shape, interaction potential) and predicting the resulting assembled structures.^77,138–144 Inverse design, in contrast, begins with desired material properties, translates them into a target structure, and then seeks the building blocks and interaction rules that will yield this structure through self-assembly. This approach is particularly challenging because of the combinatorial complexity of the design space and the nonlinear, often stochastic nature of self-assembly pathways. Unlike forward modelling, which follows deterministic rules from cause to effect, inverse design involves many-to-one mapping and is sensitive to small perturbations in interaction parameters, making traditional trial-and-error approaches inefficient. Machine learning provides a powerful framework to overcome these challenges by efficiently exploring high-dimensional parameter spaces and learning complex inverse mappings from structure to interaction design.¹⁴⁵

As shown in Fig. 10(a), a typical ML-based inverse design pipeline begins with parameter sampling from a distribution and simulation of candidate systems. The resulting configurations are scored using CNNs trained to evaluate phase identity from features such as diffraction patterns. Samples with higher likelihoods of matching the target structure (QC12 quasicrystals) are ranked with higher fitness scores. The parameter distribution is then updated to focus exploration toward regions yielding high-fitness assemblies. This closed-loop optimization continues until convergence on optimal design parameters.¹³¹

Fig. 10 Inverse design of self-assembly using fitness-driven learning. (a) A generative model samples assembly parameters from a probability distribution, evaluates the resulting structures via convolutional neural networks trained on diffraction patterns, and updates the distribution toward high-fitness regions.¹³¹ (b) The approach enables discovery of design parameters for complex target structures such as quasicrystals (QC12), identified through iterative refinement of the design space.¹³¹

The approach illustrated in Fig. 10(b) successfully reverse-engineers quasicrystalline order from a soft repulsive potential, with the ML loop learning interaction rules that favour QC12 phases. Representative structures and their diffraction patterns (Fig. 10(b)) confirm that ML-guided inverse design can recover complex, non-periodic assemblies that are difficult to access through intuition alone. Such frameworks are extensible to experimental colloidal systems, offering a path toward programmable materials design driven by data.

4.4. Limitations and open questions

While machine learning has been widely applied to simulation data in colloidal systems, its application to experimental colloidal data remains relatively nascent. Experimental datasets introduce additional complexity, such as noise, imaging artifacts, and heterogeneous data formats that pose unique challenges. Addressing these barriers is essential to fully unlock ML's potential in experimental soft matter research.

A fundamental challenge lies in the transferability of models across different experimental systems. ML models trained on a specific dataset, such as particles imaged under a particular microscope, using a specific colloidal formulation or interaction potential, often fails to perform reliably when applied to other systems. Variations in particle size, polydispersity, surface chemistry, solvent conditions, and imaging resolution all affect the features that the model learns. This lack of robustness limits the model's utility and underscores the need for more generalizable architectures or domain adaptation strategies that can bridge across experimental platforms. A further challenge arises from the limitations of a single data source. ML models trained exclusively on real-space trajectories may not be robust enough for the entire colloidal size range, particularly for systems below the optical resolution limit. To create more complete and transferable framework, it is crucial to integrate descriptors from other techniques. For nanoscale systems where particle tracking is not possible, descriptors from methods like neutron and X-ray scattering can provide crucial structural information regarding how colloids spatially organize or aggregate. Furthermore, incorporating data from molecular simulations and theory can generate descriptors that extend beyond direct experimental accessibility and help bridge disparate length scales, leading to more comprehensive and powerful ML models.

Closely related is the issue of interpretability. Many powerful ML models, especially deep neural networks, operate as “black boxes” and learn internal representations that are difficult to map back onto physically meaningful quantities. For instance, a model might correctly classify crystalline versus amorphous regions but provide no insight into which geometric or topological features drive the decision. In colloidal science, where the goal is often to gain mechanistic understanding, not just prediction, this lack of interpretability restricts the scientific value of ML outputs. Developing interpretable models or applying techniques such as saliency mapping, feature attribution, or symbolic regression may help bridge this gap.

A further consideration is the interpretability of black-box models. Many powerful ML architectures, especially deep neural networks such as CNNs, often provide predictions without clear insight into the underlying decision process. However, in experimental colloidal science, the input variables used for training such as local density, bond-order parameters, or strain, frequently carry direct physical meaning. This opens the door for interpretability methods that quantify the relative importance of features and connect model outputs back to physically relevant descriptors. For example, Shapley Additive Explanations (SHAP) can attribute predictive power to individual variables, thereby highlighting which structural or dynamical quantities most strongly influence classification or regression outcomes.^146–148 Integrating such approaches not only enhances transparency but also ensures that ML frameworks contribute mechanistic understanding, even when build on complex architectures like CNNs.

Bridging the gap between simulation-trained models and experimental data remains a major hurdle. Simulation data are typically clean and fully labelled, whereas experimental data are noisy and incomplete. Overcoming this gap may require sim-to-real transfer strategies, such as training models on hybrid datasets, applying noise injection during simulation, or using domain randomization to improve robustness to real-world variability.

Finally, there is a risk of overfitting to synthetic or curated datasets, particularly when models are trained on limited simulation data that do not reflect the variability of experimental conditions. This can be mitigated through diverse training sets, data augmentation, and cross-domain benchmarking, ensuring that models capture general trends rather than overfitting to idealized scenarios.

Despite these limitations, ML opens several exciting directions for colloid science. Machine learning is uniquely suited to uncovering subtle or hidden patterns in high-dimensional experimental datasets, potentially revealing new intermediate phases, deformation mechanisms, or assembly pathways. It also enables scalable and quantitative analysis of massive datasets, especially in data-intensive experiments. Once trained, predictive ML models can forecast structural stability, self-assembly outcomes, or mechanical response under varying conditions. These models offer fast hypothesis testing and materials screening capabilities.

Furthermore, ML can provide experimental feedback to improve or challenge existing theories, especially in regimes where classical models, like nucleation theory, are inadequate. Finally, integrating ML with inverse design approaches can accelerate rational materials development by identifying interaction parameters or guiding experimental design toward desired outcomes. This is particularly valuable when considering the importance of incorporating data from failed experiments. Unlike simulations that produce clean, successful outcomes, experimental data often include noise, artifacts, and results from trials that did not achieve the desired goal. By training models on these negative results, we can reduce data bias and help the model learn the boundaries of a system's behaviour, leading to more robust and generalized predictions. This approach accelerates the design of future experiments by guiding researchers away from unproductive regions of the parameter space and toward more promising conditions.

5. Concluding remarks and outlook

While ML has become increasingly established in simulation-based materials modelling, its direct application to experimental colloidal data remains in an early stage. This disconnect is notable, given the distinctive advantages offered by colloidal systems. These systems enable real-space, real-time access to particle-level structure, dynamics, and mechanical behaviour under precisely tuneable and reproducible conditions. Such capabilities render colloids highly suitable for the development of interpretable and transferable models in data-centric materials research.

Colloidal experiments provide high-fidelity, high-dimensional datasets that capture microscale phenomena with a level of detail rarely attainable in atomic or molecular systems. Techniques such as confocal microscopy and traction rheoscopy yield reproducible, physically meaningful data, presenting an exceptional intersection between experimental observability and algorithmic inference.

Rather than viewing colloids as approximate analogues of atomic systems, their true value lies in their ability to generate structured, physically grounded descriptors. These include measures of local structural order, dynamical rearrangements, and stress distributions, resolved at the single-particle level. Such descriptors serve as robust inputs for supervised, unsupervised, and hybrid learning approaches, facilitating both prediction and mechanistic interpretation.

Importantly, colloidal systems complement existing tools in materials-focused ML by providing data that are both experimentally grounded and highly interpretable. While simulation and imaging-based approaches offer valuable insights, they often face challenges related to labelling and mechanistic transparency. Colloidal datasets, in contrast, support model development through direct access to particle-level interactions and structure–property relationships. Owing to their transparent structure–property relationships, colloidal datasets support model development that is not only predictive but also auditable and experimentally verifiable. This stands in contrast to many black-box models built from bulk measurements or coarse image embeddings.

The experimental versability of colloids further enables systematic perturbation for evaluating model performance. By varying interaction strength, volume fraction, or external fields, researchers can map model sensitivity and failure modes. As such, colloids provide a controlled platform for benchmarking generalization and advancing algorithmic robustness.

In the longer term, colloids may not be the materials of final interest, but they can be indispensable in building the foundations for trustworthy, physics-aware ML. Their role is akin to that of well-designed model organisms in biology: not the endpoint of inquiry, but a fertile ground for generating hypotheses, training algorithms, and validating mechanisms under well-controlled and observable conditions. When paired with advances in differentiable programming, simulation-aware architectures, and inverse design loops, colloids could help transform ML from a black-box accelerator into a transparent, hypothesis-driven research partner.

In summary, colloidal systems represent a high-leverage intersection between experimental resolution and algorithmic learning. Their ability to deliver structured descriptors across structural, dynamic, and mechanical domains—coupled with their compatibility with real-time imaging and systematic control—makes them uniquely suited to guide the development of next-generation materials intelligence. To unlock this potential, we must recognize colloids not simply as illustrative models of matter, but as data-rich training grounds for building predictive, interpretable, and transferable frameworks that connect microscopic rules to macroscopic functionality.

Author contributions

N. Kang: conceptualization, investigation, writing (original draft). Y. Joo: visualization, data curation. H. An: validation, writing (review & editing). H. Hwang: conceptualization, supervision, writing (original draft, review, and editing), funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Acknowledgements

This research was supported by National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (No. 2025-02215502) and the POSCO Science Fellowship of POSCO TJ Park Foundation.

References

1. W. Poon, Science, 2004, 304, 830–831.
2. P. N. Pusey and W. Van Megen, Nature, 1986, 320, 340–342.
3. W. van Megan, S. M. Underwood, R. H. Ottewill, N. S. J. Williams and P. N. Pusey, Faraday Discuss. Chem. Soc., 1987, 83, 47–57.
4. W. B. Rogers and J. C. Crocker, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 15687–15692.
5. R. Sahu, M. Sharma, P. Schall, S. Maitra Bhattacharyya and V. Chikkadi, Proc. Natl. Acad. Sci. U. S. A., 2024, 121, e2405515121.
6. E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield and D. A. Weitz, Science, 2000, 287, 627–631.
7. S. Park, H. Hwang and S.-H. Kim, J. Am. Chem. Soc., 2022, 144, 18397–18405.
8. H. Hwang, D. A. Weitz and F. Spaepen, Proc. Natl. Acad. Sci. U. S. A., 2019, 116, 1180–1184.
9. M. Liao, X. Xiao, S. T. Chui and Y. Han, Phys. Rev. X, 2018, 8, 021045.
10. F. Wang, D. Zhou and Y. Han, Adv. Funct. Mater., 2016, 26, 8903–8919.
11. Y. Wang, Y. Wang, X. Zheng, É. Ducrot, J. S. Yodh, M. Weck and D. J. Pine, Nat. Commun., 2015, 6, 7253.
12. Y. Peng, F. Wang, Z. Wang, A. M. Alsayed, Z. Zhang, A. G. Yodh and Y. Han, Nat. Mater., 2015, 14, 101–108.
13. W. Qi, Y. Peng, Y. Han, R. K. Bowles and M. Dijkstra, Phys. Rev. Lett., 2015, 115, 185701.
14. Z. Wang, F. Wang, Y. Peng and Y. Han, Nat. Commun., 2015, 6, 6942.
15. B. Li, D. Zhou and Y. Han, Nat. Rev. Mater., 2016, 1, 1–13.
16. M. Dijkstra and E. Luijten, Nat. Mater., 2021, 20, 762–773.
17. Y. Shelke, S. Marín-Aguilar, F. Camerin, M. Dijkstra and D. J. Kraft, J. Colloid Interface Sci., 2023, 629, 322–333.
18. M. He, J. P. Gales, É. Ducrot, Z. Gong, G.-R. Yi, S. Sacanna and D. J. Pine, Nature, 2020, 585, 524–529.
19. E. Duguet, A. Désert, A. Perro and S. Ravaine, Chem. Soc. Rev., 2011, 40, 941–960.
20. R. Soto and R. Golestanian, Phys. Rev. Lett., 2014, 112, 068301.
21. H. Löwen, Europhys. Lett., 2018, 121, 58001.
22. S. Tang, Z. Hu, B. Zhou, Z. Cheng, J. Wu and M. Marquez, Macromolecules, 2007, 40, 9544–9548.
23. Z. Wang, F. Wang, Y. Peng, Z. Zheng and Y. Han, Science, 2012, 338, 87–90.
24. T. H. Zhang and X. Y. Liu, Chem. Soc. Rev., 2014, 43, 2324–2347.
25. L. Himanen, A. Geurts, A. S. Foster and P. Rinke, Adv. Sci., 2019, 6, 1900808.
26. K. Rajan, Mater. Today, 2005, 8, 38–45.
27. L. Zdeborová, Nat. Phys., 2017, 13, 420–421.
28. T. Mueller, A. G. Kusne and R. Ramprasad, Rev. Comput. Chem., 2016, 29, 186–273.
29. K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev and A. Walsh, Nature, 2018, 559, 547–555.
30. A. P. Bartók, S. De, C. Poelking, N. Bernstein, J. R. Kermode, G. Csányi and M. Ceriotti, Sci. Adv., 2017, 3, e1701816.
31. J. Schmidt, T. F. Cerqueira, A. H. Romero, A. Loew, F. Jäger, H.-C. Wang, S. Botti and M. A. Marques, Mater. Today Phys., 2024, 48, 101560.
32. R. Ramprasad, R. Batra, G. Pilania, A. Mannodi-Kanakkithodi and C. Kim, npj Comput. Mater., 2017, 3, 54.
33. P. Xu, X. Ji, M. Li and W. Lu, npj Comput. Mater., 2023, 9, 42.
34. Y. A. Alghofaili, M. Alghadeer, A. A. Alsaui, S. M. Alqahtani and F. H. Alharbi, J. Phys. Chem. C, 2023, 127, 16645–16653.
35. A. Merchant, S. Batzner, S. S. Schoenholz, M. Aykol, G. Cheon and E. D. Cubuk, Nature, 2023, 624, 80–85.
36. M. L. Green, C. Choi, J. Hattrick-Simpers, A. Joshi, I. Takeuchi, S. Barron, E. Campo, T. Chiang, S. Empedocles and J. Gregoire, Appl. Phys. Rev., 2017, 4, 011105.
37. F. Schmid, ACS Polym. Au, 2022, 3, 28–58.
38. A. Banerjee, M. Hooten, N. Srouji, R. Welch, J. Shovlin and M. Dutt, Front. Soft Matter., 2024, 4, 1361066.
39. B. R. Duschatko, J. Vandermause, N. Molinari and B. Kozinsky, npj Comput. Mater., 2024, 10, 9.
40. G. Zaldivar, Y. A. Perez Sirkin, G. Debais, M. Fiora, L. L. Missoni, E. Gonzalez Solveyra and M. Tagliazucchi, ACS Omega, 2022, 7, 38109–38121.
41. J. Carrasquilla and R. G. Melko, Nat. Phys., 2017, 13, 431–434.
42. J. Venderley, V. Khemani and E.-A. Kim, Phys. Rev. Lett., 2018, 120, 257204.
43. S. S. Funai and D. Giataganas, Phys. Rev. Res., 2020, 2, 033415.
44. L. Wang, Phys. Rev. B, 2016, 94, 195105.
45. S. J. Wetzel, Phys. Rev. E, 2017, 96, 022140.
46. E. Boattini, M. Dijkstra and L. Filion, J. Chem. Phys., 2019, 151, 154901.
47. E. Boattini, N. Bezem, S. N. Punnathanam, F. Smallenburg and L. Filion, J. Chem. Phys., 2020, 153, 064902.
48. C. Dai and S. C. Glotzer, J. Phys. Chem. B, 2020, 124, 1275–1284.
49. W. F. Reinhart, A. W. Long, M. P. Howard, A. L. Ferguson and A. Z. Panagiotopoulos, Soft Matter, 2017, 13, 4733–4745.
50. L. Yao, Z. Ou, B. Luo, C. Xu and Q. Chen, ACS Cent. Sci., 2020, 6, 1421–1430.
51. L. Ding, Y. Chen and C. Do, Appl. Crystallogr., 2025, 58, 992–999.
52. A. A. Moud, Colloid Interface Sci. Commun., 2022, 47, 100595.
53. E. D. Cubuk, S. S. Schoenholz, J. M. Rieser, B. D. Malone, J. Rottler, D. J. Durian, E. Kaxiras and A. J. Liu, Phys. Rev. Lett., 2015, 114, 108001.
54. S. S. Schoenholz, E. D. Cubuk, D. M. Sussman, E. Kaxiras and A. J. Liu, Nat. Phys., 2016, 12, 469–471.
55. F. P. Landes, G. Biroli, O. Dauchot, A. J. Liu and D. R. Reichman, Phys. Rev. E, 2020, 101, 010602.
56. S. S. Schoenholz, E. D. Cubuk, E. Kaxiras and A. J. Liu, Proc. Natl. Acad. Sci. U. S. A., 2017, 114, 263–267.
57. P. Geiger and C. Dellago, J. Chem. Phys., 2013, 139, 164105.
58. P. Rajak, A. Krishnamoorthy, A. Mishra, R. Kalia, A. Nakano and P. Vashishta, npj Comput. Mater., 2021, 7, 108.
59. R. Jain, S. Jain, S. K. Dewangan, L. K. Boriwal and S. Samal, J. Alloys Metall. Syst., 2024, 8, 100110.
60. C. J. Bartel, A. Trewartha, Q. Wang, A. Dunn, A. Jain and G. Ceder, npj Comput. Mater., 2020, 6, 97.
61. J. Riebesell, R. E. Goodall, P. Benner, Y. Chiang, B. Deng, G. Ceder, M. Asta, A. A. Lee, A. Jain and K. A. Persson, Nat. Mach. Intell., 2025, 7, 836–847.
62. M. Mika, N. Tomczak, C. Finney, J. Carter and A. Aitkaliyeva, J. Materiomics, 2024, 10, 896–905.
63. X. Xu, Q. Wei, H. Li, Y. Wang, Y. Chen and Y. Jiang, Phys. Rev. E, 2019, 99, 043307.
64. E. Boattini, S. Marín-Aguilar, S. Mitra, G. Foffi, F. Smallenburg and L. Filion, Nat. Commun., 2020, 11, 5479.
65. S. Sgroi, G. M. Palma and M. Paternostro, Phys. Rev. Lett., 2021, 126, 020601.
66. C. Karpovich, E. Pan and E. A. Olivetti, npj Comput. Mater., 2024, 10, 287.
67. G. Tom, S. P. Schmid, S. G. Baird, Y. Cao, K. Darvish, H. Hao, S. Lo, S. Pablo-García, E. M. Rajaonson and M. Skreta, Chem. Rev., 2024, 124, 9633–9732.
68. J. Cai, X. Chu, K. Xu, H. Li and J. Wei, Nanoscale Adv., 2020, 2, 3115–3130.
69. I. Papadimitriou, I. Gialampoukidis, S. Vrochidis and I. Kompatsiaris, Comput. Mater. Sci., 2024, 235, 112793.
70. V. Prasad, D. Semwogerere and E. R. Weeks, J. Phys.: Condens. Matter, 2007, 19, 113102.
71. H. Carstensen, V. Kapaklis and M. Wolff, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2015, 92, 012303.
72. D. Bochicchio, A. Videcoq and R. Ferrando, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2013, 87, 022304.
73. B. Ackerson, Phase transitions in colloidal suspensions, CRC Press, 1990.
74. H. Löwen, Phys. Rep., 1994, 237, 249–324.
75. V. J. Anderson and H. N. Lekkerkerker, Nature, 2002, 416, 811–815.
76. B. J. Alder and T. E. Wainwright, J. Chem. Phys., 1957, 27, 1208.
77. V. N. Manoharan, Science, 2015, 349, 1253751.
78. P. G. Bolhuis, D. Frenkel, S.-C. Mau and D. A. Huse, Nature, 1997, 388, 235–236.
79. Z. Zheng, F. Wang and Y. Han, Phys. Rev. Lett., 2011, 107, 065702.
80. E. Zaccarelli, C. Valeriani, E. Sanz, W. Poon, M. Cates and P. Pusey, Phys. Rev. Lett., 2009, 103, 135704.
81. B. Van Der Meer, W. Qi, R. G. Fokkink, J. Van Der Gucht, M. Dijkstra and J. Sprakel, Proc. Natl. Acad. Sci. U. S. A., 2014, 111, 15356–15361.
82. Y. Gao and M. L. Kilfoil, Opt. Express, 2009, 17, 4685–4704.
83. J. C. Crocker and D. G. Grier, J. Colloid Interface Sci., 1996, 179, 298–310.
84. S. S. Blackman and R. Popoli, Design and analysis of modern tracking systems, Artech House, Norwood, MA, 1999.
85. A. Kawafi, L. Kürten, L. Ortlieb, Y. Yang, A. M. Amieva, J. Hallett and C. P. Royall, Soft Matter, 2025, 21, 6338–6352.
86. D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch and M. Unser, Methods, 2017, 115, 28–41.
87. J. Z. Terdik, D. A. Weitz and F. Spaepen, Phys. Rev. E, 2024, 110, 024606.
88. P. J. Steinhardt, D. R. Nelson and M. Ronchetti, Phys. Rev. B: Condens. Matter Mater. Phys., 1983, 28, 784.
89. U. Gasser, A. Schofield and D. Weitz, J. Phys.: Condens. Matter, 2002, 15, S375.
90. U. Gasser, E. R. Weeks, A. Schofield, P. Pusey and D. Weitz, Science, 2001, 292, 258–262.
91. H. Hwang, D. A. Weitz and F. Spaepen, Proc. Natl. Acad. Sci. U. S. A., 2020, 117, 25225–25229.
92. R. Alert, P. Tierno and J. Casademunt, Proc. Natl. Acad. Sci. U. S. A., 2017, 114, 12906–12909.
93. C. Mayer, E. Zaccarelli, E. Stiakakis, C. Likos, F. Sciortino, A. Munam, M. Gauthier, N. Hadjichristidis, H. Iatrou and P. Tartaglia, Nat. Mater., 2008, 7, 780–784.
94. H. Zhang, Q. Zhang, F. Liu and Y. Han, Phys. Rev. Lett., 2024, 132, 078201.
95. Q. Zhang, W. Li, K. Qiao and Y. Han, Sci. Adv., 2023, 9, eadf1101.
96. A. Baranyai and D. J. Evans, Phys. Rev. A: At., Mol., Opt. Phys., 1989, 40, 3817.
97. H. Tanaka, T. Kawasaki, H. Shintani and K. Watanabe, Nat. Mater., 2010, 9, 324–331.
98. V. D. Nguyen, S. Faber, Z. Hu, G. H. Wegdam and P. Schall, Nat. Commun., 2013, 4, 1584.
99. G. L. Hunter and E. R. Weeks, Rep. Prog. Phys., 2012, 75, 066501.
100. W. K. Kegel and A. van Blaaderen, Science, 2000, 287, 290–293.
101. A. Einstein, Ann. Phys., 1905, 4.
102. E. R. Weeks, ACS Macro Lett., 2017, 6, 27–34.
103. G. Dunderdale, S. Ebbens, P. Fairclough and J. Howse, Langmuir, 2012, 28, 10997–11006.
104. L. Van Hove, Phys. Rev., 1954, 95, 249.
105. C. Patrick Royall, S. R. Williams, T. Ohtsuka and H. Tanaka, Nat. Mater., 2008, 7, 556–561.
106. N. Gnan and E. Zaccarelli, Nat. Phys., 2019, 15, 683–688.
107. V. Martinez, G. Bryant and W. Van Megen, Phys. Rev. Lett., 2008, 101, 135702.
108. D. Weidig and J. Wagner, Soft Matter, 2024, 20, 8897–8908.
109. B. Mei, Y. Lu, L. An and Z.-G. Wang, Phys. Rev. E, 2019, 100, 052607.
110. F. Lindemann, Phys. Z., 1910, 11, 609–612.
111. W. Li, Y. Peng, T. Still, A. Yodh and Y. Han, Rep. Prog. Phys., 2024, 88, 010501.
112. Y. Peng, W. Li, T. Still, A. G. Yodh and Y. Han, Nat. Commun., 2023, 14, 4905.
113. K. Jensen, D. A. Weitz and F. Spaepen, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2014, 90, 042305.
114. N. Y. Lin, M. Bierbaum and I. Cohen, Phys. Rev. Lett., 2017, 119, 138001.
115. P. Schall, D. A. Weitz and F. Spaepen, Science, 2007, 318, 1895–1899.
116. D. Chen, D. Semwogerere, J. Sato, V. Breedveld and E. R. Weeks, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2010, 81, 011403.
117. R. Besseling, L. Isa, E. R. Weeks and W. C. Poon, Adv. Colloid Interface Sci., 2009, 146, 1–17.
118. N. Y. Lin, M. Bierbaum, P. Schall, J. P. Sethna and I. Cohen, Nat. Mater., 2016, 15, 1172–1176.
119. N. F. Carnahan and K. E. Starling, J. Chem. Phys., 1969, 51, 635–636.
120. R. Ottewill, Langmuir, 1989, 5, 4–11.
121. J. F. Brady, J. Chem. Phys., 1993, 98, 3335–3341.
122. A. Stukowski, Modell. Simul. Mater. Sci. Eng., 2009, 18, 015012.
123. S. Kim, I. Svetlizky, D. A. Weitz and F. Spaepen, Nature, 2024, 630, 648–653.
124. R. B. Sills, N. Bertin, A. Aghaei and W. Cai, Phys. Rev. Lett., 2018, 121, 085501.
125. V. Shenoy, R. Kukta and R. Phillips, Phys. Rev. Lett., 2000, 84, 1491.
126. P. Franciosi, M. Berveiller and A. Zaoui, Acta Metall., 1980, 28, 273–283.
127. W. S. Slaughter, The linearized theory of elasticity, Springer Science & Business Media, 2012.
128. A. Lizano and X. Tang, Soft Matter, 2023, 19, 3450–3457.
129. E. C. Kim, D. J. Chun, C. B. Park and B. J. Sung, Phys. Rev. E, 2023, 108, 044602.
130. H. Doi, K. Z. Takahashi, K. Tagashira, J.-I. Fukuda and T. Aoyagi, Sci. Rep., 2019, 9, 16370.
131. G. M. Coli, E. Boattini, L. Filion and M. Dijkstra, Sci. Adv., 2022, 8, eabj6731.
132. C. Dietz, T. Kretz and M. Thoma, Phys. Rev. E, 2017, 96, 011301.
133. E. Boattini, M. Ram, F. Smallenburg and L. Filion, Mol. Phys., 2018, 116, 3066–3075.
134. R. Mao, J. O’Leary, A. Mesbah and J. Mittal, JACS Au, 2022, 2, 1818–1828.
135. F. M. Dietrich, X. R. Advincula, G. Gobbo, M. A. Bellucci and M. Salvalaglio, J. Chem. Theory Comput., 2023, 20, 1600–1611.
136. A. N. Filiatraut, J. R. Mianroodi, N. H. Siboni and M. B. Zanjani, J. Appl. Phys., 2023, 134, 234702.
137. Q.-Z. Zhu, C. X. Du, E. M. King and M. P. Brenner, Phys. Rev. Res., 2024, 6, L042057.
138. S. C. Glotzer and M. J. Solomon, Nat. Mater., 2007, 6, 557–562.
139. S. Sacanna, D. J. Pine and G.-R. Yi, Soft Matter, 2013, 9, 8096–8106.
140. A. Yodh, K.-H. Lin, J. C. Crocker, A. Dinsmore, R. Verma and P. Kaplan, Philos. Trans. R. Soc., A, 2001, 359, 921–937.
141. Y. Huang, C. Wu, J. Chen and J. Tang, Angew. Chem., 2024, 136, e202313885.
142. M. A. Boles, M. Engel and D. V. Talapin, Chem. Rev., 2016, 116, 11220–11289.
143. Z. Li, Q. Fan and Y. Yin, Chem. Rev., 2021, 122, 4976–5067.
144. R. K. Cersonsky, G. van Anders, P. M. Dodd and S. C. Glotzer, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, 1439–1444.
145. B. A. Lindquist, R. B. Jadrich and T. M. Truskett, J. Chem. Phys., 2016, 145, 111101.
146. S. M. Lundberg and S.-I. Lee, Adv. Neural Inf. Process. Syst., 2017, 30, 4765–4774.
147. C. Molnar, Interpretable machine learning, https://Lulu.com, 2020.
148. X. Zhao and L. Fu, Ann. Phys., 2019, 410, 167938.

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