Gradient-based Active Learning For Intelligent Discovery Of Colloidal Phase Diagrams

Abstract

Rapid and accurate prediction of the colloidal phase diagrams is necessary for controlling their structure and properties. Mapping these multi-dimensional phase diagrams with molecular dynamics (MD) is costly, especially when sharp, localized transition boundaries demand dense sampling to resolve the boundaries. We target this challenge by actively learning the boundary where the order parameter---the number of nearest neighbours, \(N_{nn}\)---undergoes an abrupt change. We describe colloids interacting \textit{via} isotropic pair potentials with tunable range of interaction and aim to identify the boundary between the dilute and condensed phases. We model \(N_{nn}=f(\mathbf{x})\) with a Gaussian process (GP) and derive a gradient-aware acquisition strategy that prioritizes locations with large and/or uncertain spatial derivatives of the GP posterior. The gradient-aware strategy is based on the thermodynamic principle of large susceptibility, i.e., large derivative of the order parameter, at phase boundaries. A simple ellipse-based exclusion heuristic helps spread acquisitions along the boundary manifold. Across 1D and 2D planes of the phase diagram, the proposed strategy localizes phase boundaries accurately with significantly fewer MD runs than dense grid search and outperforms random acquisition or standard acquisition strategies unaware of the gradient of the GP. The framework can be readily extended to higher-dimensional space and support multi-fidelity MD simulations, providing a practical route to sample-efficient and physics-aligned discovery of colloidal phase diagrams.