Application of neural network in metal adsorption using biomaterials (BMs): a review †

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Introduction
Growing population, urbanization, and changing climate cycles stress water resources and public water supplies.The United Nations reported that 2.3 billion people live in water-scarce zones worldwide. 1Public health and economic tensions from water scarcity will be exacerbated in regions with water tainted with metal contaminants.6][17][18][19][20][21][22][23] The selection and fabrication of sustainable adsorbents for the eradication of water pollutants include the following criteria: (1) it should be inexpensive and (2) simple to synthesize in large quantities, (3)  it should demonstrate high adsorption capacity and most importantly, (4) it should cause no harm to the environment.adsorption and desorption cycles, enabling their use for heavy metal ions removal. 31The porous texture of biomaterials speeds up the transport of metal ions, while the presence of phenolic, carbonyl, amide and amine-containing functional groups in biomaterials facilitate metal ion adsorption through surface complexation. 32,33In addition, biomaterial systems have been engineered using various surface functionalization and physical alterations to tailor their surface chemistry and enhance their adsorptive capacity.For instance, our research team has prepared eco-friendly cellulose beads impregnated with nano iron oxide for thorium and arsenic retrieval; 34,35 synthesized cost-effective cellulose nanobers and functionalized with camphor soot carbon nanoparticles for uranium extraction; 36 crosslinked starch with polyvinyl alcohol for oil-water separation; 37 electrospun nano bres for adsorption of metal ions; [38][39][40][41] developed composites from agro-wastes for removal of metal and dyes. 42The details of distinct physical and chemical modications of biomaterials are illustrated in Fig. S1.† The BMs' performance is greatly affected by environmental conditions (pH, temperature), initial metal concentration, and the structure of the biomaterial.Laboratory experiments have been used to discover high-performing BMs; however, these studies are costly for time and resources.Accordingly, modelling techniques could offer time-and resource-saving efficiency in predicting the performance of BMs for full-scale application. 43,446][47][48] The joint role of spectroscopic analysis and RSM has been applied to enumerate the adsorptive removal of zinc (Zn(II)), cobalt (Co(II)) and nickel (Ni(II)). 49Since these adsorption systems exhibit nonlinear adsorptive behaviours, it would be inappropriate to characterize them using conventional statistical models.][52][53] Studies in the past stipulated the removal efficiency of metals using various articial intelligence (AI) models.For example, Bhagat et al., 2020 examined the application of distinct AI models like kernel, evolutionary, black box, fuzzy and hybrid models for optimizing heavy metal removal. 206ather than illustrating the mathematical concepts necessary for automation, the author highlighted treatment procedures such as occulation, coagulation, membrane ltration, biosorption, proposed prediction models, input and output variables, and distinct metrics for comparing model performance.Alam et al., 2022; Reynel-Ávila et al., 2022 categorized AI technologies and reported their use in the remediation of organic and inorganic contaminants. 207,208Whereas Yaseen et al., 2021 discussed the utility of AI in simulating soil and water bodies contaminated with metals. 209The utilization of classical adsorption models, multicomponent adsorption, sensitivity analysis, and progression in ANN frameworks were not discussed earlier in detail for evaluating kinetics, isotherms, and thermodynamic parameters of adsorption.
This review briey explains the main biomaterial alteration processes and discusses conventional adsorption investigations in conjunction with ANN modelling.Then, we address the preand post-processing methods involved in constructing ANN models and show statistics of datasets considered for optimizing metal adsorption on biomaterial systems.We describe current advancements in the ANN framework for single and multi-metal adsorption process optimization and related improvements in hybridizing isotherm, kinetics, and breakthrough curves.Next, advances in thermodynamic parameter estimations are reported to understand the nature of the adsorption process.The sensitivity analysis of ANN has also been described to comprehend the relative inuence of individual and group of adsorption factors on anticipated efficiency.Towards the end, the review highlights signicant challenges and advancements in the eld of ANN technology for metal remediation.

Experimental studies and dataset of metals adsorption on BMs
A given biomaterial's interaction with metal adsorbates depends on its functional groups, the engineered surface of biomaterials, pH and temperature conditions, and physical or chemical changes in the conguration that inuence biomaterials' morphology, pore size distribution, and elemental compositions.However, biomaterials without modication have constraints regarding recovery and recycling.Because of their poor porosity and limited adsorption sites, pristine biomaterials exhibit low adsorption efficacy. 54hus, the engineered modications and surface alterations of the biomaterial matrix become necessary to achieve greater adsorption capacities.Research reports the conversion of natural biomaterials into beads, foams, and nanobers to attain better pore size distribution and durability.4][65][66] The reutilization of saturated biomaterials into value-added products has been reported in detail by authors in their earlier research. 7The experimental adsorption studies that depict various aspects of metals adsorption relevant for ANN modelling are given below:

Adsorption kinetics
Adsorption kinetics gives vital information about the associated mechanism and equilibrium time required to sequester maximum metal impurities from an aqueous solution.The period of contact (CT) between the biomaterial and metal adsorbate and equilibrium time (t e ) corresponding to specic metal concentrations (C o ) are listed in Table 1.The kinetics adsorption data using modied biomaterials tted best with the pseudo-second-order equation, where the values of kinetic model parameters differ regarding when the equilibrium time is reached.The experimentally obtained details (initial metals concentration, contact time and equilibrium time) will aid in developing ANN-driven kinetic models for predicting the signicant kinetic parameters and uptake capacity detailed further in Section 5.

Adsorption isotherms
Adsorption isotherm models describe the maximum adsorption capacity at equilibrium adsorption conditions.Table 2 displays the adsorption isotherm data for modied biomaterials for different metal ions.The Langmuir isotherm best characterized the adsorbent-adsorbate interactions for biomaterials, suggesting monolayer adsorption of metal ions on the biomaterial surface.In general, the use of linear empirical models to evaluate the isotherm parameters of the nonlinear adsorption process is becoming obsolete as it does not explicitly describe the simultaneous adsorption pattern over a wide range of operating temperatures and metal ion concentration. 82urthermore, because most industrial wastewaters contain numerous metal pollutants, single-species models do not adequately reect the complex propensity of multicomponent adsorption.For this purpose, the isotherm parameters evaluation using hybridizing isotherms with ANN, as discussed in Section 5, is gaining popularity.

Thermodynamics
Thermodynamic parameters offer insights into the impact of changing environmental conditions (i.e.temperature) on the nature of the adsorption process using modied biomaterials.Table 3 details the adsorption process's temperature range, feasibility, and nature.The data will aid in modelling thermodynamic conditions for predicting thermodynamic parameters (e.g., Gibbs free energy changes) across a wide range of adsorption conditions, as discussed in Section 5.

Adsorption data set based on BMs and pre-processing
The biomaterials in the current review included cellulosic, alginate and chitosan-based biomaterials.Compared to other polysaccharides, plant and agriculture-based biomaterials have been extensively modelled for metal remediation purposes (refer to ESI, S2 †).3,84 The physicochemical features of the reviewed modied biomaterial systems were determined by different analytical techniques such as BET, FTIR and SEM-EDS.The morphology of some of the modied BMSs under a scanning electron microscope is shown in Fig. S2.† Experimental data is an essential prerequisite in processing the ANN framework.The details of the diverse dataset, including the characteristics of biomaterials, environmental conditions (temperature, pH) and process variables, are given in Section S2. † The experimental dataset contained 15 variables,   including initial concentration (C 0 ), pH solution (pH), temperature (T), biomaterial characteristics (surface area, particle size), contact time (CT), bed depth (BD), ow rate (FR), agitation speed (AS), the volume of solution (V), pyrolysis temperature (PT), effluent concentration (EC), medium of solution (MS), bias (B), metal pollutant efficiency (MPE%) and adsorption capacity (AC).MPE % and AC were the output variables; the remaining variables were applied as input variables.A few studies used nal concentration (FC), nal pH (FpH), and change in Gibbs free energy (dG) as the output variable in conjunction with MAE% and AC.The frequency of individual variables used by researchers is illustrated in Fig. S3.† Pre-processing experimental data using Pearson's correlation matrix is carried out to analyze the relationship among adsorption variables.In the cellulose-based biomaterials, the correlation matrix showed a complex correlation between process variables. 85However, in the case of carbon-enriched BMSs, it was worth mentioning that the oxygen to carbon ratio (O : C) and the sum of oxygen and nitrogen to carbon content (O + N : C) showed an absolute correlation. 86Hence, one of these two variables was eliminated as they represented the same data from the database.The (O + N : C) variable had a better connection with the output variable over O : C; thus, it becomes a strong contender to increase the precision of the models and explain the characteristics of the dataset employed.As illustrated in Fig. 2, the boxplot shows the range of key variables considered for modelling metal adsorption on biomaterial systems.
Post-pre-processing, the complete dataset is taken and randomly divided at 70 : 30. 5870% of the data is used for training the ANN model, while 30% is used for validating and testing the performance efficiency of ANN.The distribution of the attributes (ESI, S2 †) shows a skewness in data distribution which can signicantly affect the stability and accuracy of the ANN predictive models.Therefore, the features of the dataset are normalized using the Minmax function.

ANN for modeling for metal adsorption
3.1 Layman's guide to ANN Articial Neural Networks are inspired from a biological brain conceptual model to solve complex problems. 87Consider how a human brain distinguishes between different people: every human has a similar overall structure (e.g., two eyes, two ears, one nose, etc.), yet we can recognize people easily because learnings in the brain are intuitive.Instead of learning the face structure to identify people, it discovers the deviation of the face from a reference face, for example, 'how different one's nose is from the generic nose, which is then quantied as a signal with a specic strength'.Likewise, it learns the deviations from all parts of the face from a reference base case, combines these variations into a new dimension, and nally gives an output, which is the recalled identity of the good-looking person in front of you.All these steps in the brain occur in a fraction of a second.A neural network uses a similar algorithm, but the articial neurons process the information using a mathematical approach (Fig. S4 †).
The ANN architecture is organized into 3 layers: (1) an input, (2) a hidden or intermediate layer, and (3) an output layer.The information is rst received by neurons in the input layer, then passed on to a set of neurons associated with single or multiple hidden layers.The job of a hidden layer is to process the information coming from input neurons using weighted connection and activation functions to calculate the output of a neuron.The data is processed from one neuron to the other, similar to the deviations learned by the human brain.The greater the outcome of a neuron, the greater would be the inuence of that input dimension.These attributes are combined in the next layer using mathematical formulations to form additional new details.When multiplied several times, this procedure develops a complex network with several connections.
The neural network learns through intuitive wisdom with the help of a learning or training mechanism.For a given set of input data, the output layer makes predictions by applying a matrix multiplication series that could be either accurate or inaccurate.Based on the output, the learning mechanism gives feedback for improving the prediction efficiency of the network.The system uses a backpropagation algorithm as a feedback mechanism to incrementally update the randomly initialized weights applied to the input data for correct predictions. 88adsorption variables containing independent and dependent parameters are collected from lab experiments compiled from the literature.The acquired database is generally divided into training, validation, and test sets.Since the adsorption data of metal ions constitute many features (as shown in Fig. 1), the associated hyperparameters of neural network function also increase, raising the model's complexity.In such scenarios, a larger proportion of data (∼70%) is kept in the training subset to make the model learn the patterns of the data, while the rest 30% of data is used for validating and testing the model performance.The network is trained to nd the optimal combinations of intermediate neurons and interior layers that minimize the prediction error or loss.The neural network is trained using backpropagation (BP) algorithms which consist of the following steps, corresponding to the steps listed in Fig. 2:

Generation of the ANN model
(1) Selection of training data from the experimental data set.
(2) Identication and division of input and output variables.
(3) Forward propagation: it takes a weighted sum of inputs (by multiplying each input variable with an assigned weight) and bias.This weighted output is then passed through an activation or transfer function, which introduces nonlinearity into the result.(For mathematical interpretation, refer to ESI, S.2.2 †).Depending on the activation function used, the outputs are normalized between either 0 and 1, −1 to +1, or 0.1 to 0.9.Table S3 † lists activation functions applied for the nonlinear transformation of adsorption data.
(4) Backpropagation: the ANN calculates the difference in error between the experimental observation and the expected model output using the gradient descent method.When the error exceeds the acceptable value, the weights are adjusted by multiplying the error by the input and the transfer function's gradient (e.g., tansig function, which is the most common) (ESI, S.2.2 †).
(5) Optimization is achieved by reducing the error between observed and model-predicted responses by varying neurons in hidden layers, transfer functions, training algorithms and iterative modication of weights assigned to links emerging from the input layer. 87,89Steps 5 and 6 (of Fig. 2) are repeated until further weight changes do not reduce errors (refer to S5.2 †).
(6) The performance of the ANN for modelling adsorption is evaluated using different statistical indices (Fig. 2 step 7, 8).The researchers most commonly used the coefficient of determination (R 2 ) and correlation coefficient (R) as efficiency evaluators, whereas Root Mean Square Error (RMSE) and Mean Square Error (MSE) are used for evaluating modelling error.The mathematical formulations of these four statistical parameters are given in S5.3.† Fig. 1 The dataset before analyzing and processing (the box plots generated using data listed in ESI, Tables S1 and S2  The illustration of the feedforward neural network (FFNN) that modelled the adsorption of the metal on biomaterials is presented in Fig. S5.†

Standalone ANN frameworks
The purpose of the optimization is to achieve the maximum metal removal efficiency and uptake capacity of biomaterials used to recover metals and other contaminants from industrial wastewater for environmental protection and water purication.The optimization pathways reported in the literature are a compilation of variables inuencing the design of adsorption systems and the adsorption process. 90The variables affecting the adsorbent modication or preparation conditions and the metal adsorption efficacy include biomaterial dose, surface type and thermal treatments.Under the batch adsorption systems, the adsorption attributes that affect the process behaviour include the initial concentration of metal pollutants, pH of the aqueous solution, volume and medium of adsorbate solution, agitation or shaker speed, temperature and contact time.In continuous column set-up, metal concentrations, bed depth and ow rate are of primary concern (Table S4 †).Some studies also included the inuence of lingo-cellulosic functional groups, particle size, and calcination temperature used to optimise biomaterial adsorbents' fabrication. 52,65,66,91,92Table 4 illustrates recent developments of ANN-based optimization methods for modelling biomaterial adsorption systems.
s described in Section 3.2, the ANN framework has been extensively implemented to optimize the variables mentioned above to attain conditions for the maximum metal adsorption efficiency or metal adsorption capacity.The details of optimal ANN architecture, activation function and modelling error corresponding to each study are depicted in Table S5.† It is to be noted that the ANN training parameters such as epoch size, learning rate, momentum and gradient inuence the optimal feedforward architecture.The data division in training, validation and testing subsets and information on maximum epochs (iterations) used is illustrated in Fig. 3

(taken from Table S5-S7 †).
Table 4 lists the recent developments in ANN frameworks for simulating metal adsorption on biomaterials.While backpropagation (BP) algorithms are prominently reported in the literature for the optimization of various adsorption variables, algorithms based on experimental designs such as the Taguchi method which use orthogonal arrays to identify critical variables that can affect the adsorption process. 93Algorithms based on 2-level factorial design (FFD) have also been employed with ANN to reduce the burden of laboratory experiments and determine the optimum process variables that can maximize metal adsorption on the biomaterials.For example, Popoola, 2019 used 2 k FFD to evaluate the optimal preparation condition of carbon-enriched biomaterial that can boost cadmium removal efficiency. 94The authors used magnetite loading, walnut shell: rice husk ratio, calcination temperature and time as variables to conduct 2 4 = 16 i.e. 16 sets of experiments.It was observed that a small set of experiments were sufficient to predict the optimal adsorbent conditions (i.e.carbonaceous biomaterial calcinated at 1000 °C for 5 hours and loaded with 10 wt% magnetite coating) that will yield maximum cadmium removal (∼97%) from aqueous solution.
The RSM has been employed to conceptualize the interaction effects among independent adsorption variables. 95RSM uses the Box-Behnken Design (BBD) to investigate the interactions between different adsorption variables, for example, initial metal concentration, pH and biomaterial dose.The BBD works as a second-order polynomial equation.][98] The RSM approach is only conned to a quadratic equation; thus ANN-based model offers broader competence to capture the complex and nonlinear behaviour of the metal adsorption process from effluents with a wide spectrum of dependent factors. 57,75,86,99,100While ANN models for metal remediation call for advanced computing abilities, Narayana et al., 2021 proposed an ANN-based graphical user interface (GUI) for experimentalists or researchers unfamiliar with computation to extract adsorption data for a particular dataset. 85

Ensemble ANN frameworks
The standalone ANN framework trains the adsorption data using the backpropagation (BP) training algorithm.Given that BP uses the gradient descent approach to update the network's  link weights, the network may converge prematurely or get stuck in local minima. 104,105Because of such drawbacks, ANNs can fall short of expected performance.7][108][109] The ow chart illustrating any metaheuristic system's general framework is given in Fig. 4. Hamidian et al., 2019 used the Symbiotic Organisms Search (SOS) algorithm in conjunction with ANN to optimize heavy metals removal (Fe(II)), Cu(II), Co(II), Cd(II) and Al(III)) using chitosan-based nanomaterials. 83The authors applied adsorbent dose, pH and initial concentration of metals as input parameters to the network.The symbiotic search algorithm (SOS) is a recently developed algorithm based on SI (Swarm Intelligence) that simulates the cooperative behaviour observed in nature among individuals.It generates a new solution using three coexisting behaviour types between paired organisms in an ecosystem: mutualism, commensalism, and parasitism.Mutualism is an interaction between two species with mutual benet, meaning both benet from the relationship.Commensalism occurs when one species forms a bond with another, and one species benets while the other is unaffected.When two species form a relationship in which one benets and the other hurts, it is referred to as parasitism.Both mutualism and commensalism focus on creating new species for the next generation.The parasitic phase prevents the search process from escaping the local minima.The ANN-SOS framework is illustrated in Fig. S6.†).The integration of ANN with SOS predicted metal removal efficiencies with R 2 > 0.9 in short computation time (50 runs) and fast convergence (<20).][112][113] Moradi et al., 2020 used a hybrid of Bayesian regularization (BR) and Grey wolf optimizer (GWO) with ANN to model Pb(II) and Co(II) adsorption on pistachio shells. 101The ANN space was initially optimized using the BR algorithm, using principles of probability distributions to prevent overtting of the ANN.The three input parameters, i.e. temperature, adsorbent dose and initial concentration of metals, were then further optimized by applying GWO to the space of BR-ANN for maximum metal ions removal.The GWO is a new global optimization approach that simulates grey wolf leadership and natural hunting. 114In GWO's hierarchy, the alpha is considered the group's dominant agent (best solution).The next subordinate to alpha includes beta (second ttest solution) and delta (third ttest solution), and omega wolf denotes the weakest solution.Additionally, three main phases of hunting, i.e. search for prey, encircle the prey and attack', have been implemented for optimization.The framework of BR-ANN-GWO is shown in Fig. S7.† The ANN-BR-GWO framework predicted the metal adsorption with considerably improved accuracy (R 2 = 0.99, RMSE = 1.1) against ANN-GWO (R 2 = 0.96, RMSE ∼2.2.GWO's robust search capability prevents the algorithm from getting trapped in a local optimum.In GWO, achieving the right balance between the ability to explore and exploit is easy, so it can effectively solve many complex problems when coupled with ANN. 115ANN-GWO has also been successfully used to predict the performance of desalination plants and crop yields, 116 to globally predict COVID-19 disease, 117 measure pan evaporation to compare irrigation water needs 118 and to prevent cyberattacks in our networks. 119rabhu et al., 2021 successfully used a Genetic algorithm (GA) to determine the recovery of chromium from alginate immobilized Sargassum in a xed bed column.GA works on the principles of Darwinian biological evolution from natural selection, where individuals are chosen from the population to serve as parents, aer which they are employed to bear the future generation's offspring. 93The population "evolves" to the best option through future generations.In Fig. S9, † the ANN-GA framework is displayed.In their study, the authors tuned the chromium concentration, bed length and ow rate to maximize the adsorption of chromium metal.ANN-GA showed better productivity (RMSE = 0.07) against Boltzmann statistical thermodynamics (Simulating Annealing (SA), RMSE = 0.8) (van Laarhoven & Aarts, 1987).The development response of ANN-GA for predicting metals adsorption showed a better statistical quality compared to traditional statistical models. 45,78,210The ability of evolutionary GA to address any optimization problems by tuning the selection mechanism and varying the values of genetic operators as per the problem makes these techniques superior to classic numerical optimizations.GA-ANN has attracted signicant attention due to its multiple advantages (i.e.simple method, robust response to changing conditions and exibility etc.) in solving real-world problems.These include predicting energy consumption in buildings, 120 detecting fatal heart disease, 121 solving hydrogeology problems 122 and optimizing machine parameters to reduce surface roughness 123 etc.The ability of GA to incorporate domain-specic knowledge into the algorithm results in a more efficient exploration of the state space of possible solutions.
Further, the two-step method for self-adapting parameters that govern evolutionary search relieves the human operator from the requirement to manually create solutions, which either consumes time or it is difficult. 124Evolutionary algorithms can be hybridized with other models to address particular real-world problems. 125g. 4 A general working scheme of a metaheuristic algorithm.
More recently, Zheng and Nguyen, 2022 have implemented Queuing Search Algorithm (QSA) to update the weights of ANN using the three main activities of humans in queuing: (i) prefer following the customer queue with prompt service.(ii) Effect of customers or employees on customer service.(iii) Impact of not maintaining the queue on customer service. 103The QSA model stimulates the queening system, as described in ref. 126, to optimize the adsorption of metals, i.e. arsenic (As(II)), cadmium (Cd(II)), nickel (Ni(II)), copper (Cu(II)), lead (Pb(II)) and zinc (Zn(II)) on carbon-enriched biomaterial.The model used initial concentration, total carbon content, pH of the solution and pyrolysis temperature as input and metals adsorption efficiency as the output.The details of the ANN-QSA optimization procedure is illustrated in Fig. S10.† The adsorption efficiency predicted by the ANN-QSA model was closer to the metal adsorption efficiency of metals (i.e.RMSE = 0.051 and RMSE = 0.074 for the training and testing datasets, respectively).The standalone ANN model predicts adsorption efficiency (i.e.RMSE = 0.076 and RMSE = 0.097 for the training and testing datasets, respectively).The QSAs have been used to optimize mechanical design problems (e.g.spur gear drive systems), 127,128 but its hybridization with ANN has been reported rst time for wastewater treatment applications.
Besides combining metaheuristic algorithms with ANN, a fuzzy model has been coupled with ANN to capture the nonlinearity of the metal adsorption process.The ANFIS structure consists of ve layers with two types of nodes: xed and adaptable (details, refer to S5.9.3 †).Nodes in the membership function layer and the next layer are tuneable, while the rest nodes are xed.The neuro-fuzzy arrangement uses ANN learning principles and logical reasoning to map input parameters through membership functions to generate output(s).The details of ANFIS architecture can be seen in S5.9.3.1 † Sadeghizadeh et al., 2019 integrated a fuzzy system with ANN to predict Pb(II) adsorption on hydroxyapatite/chitosan nanocomposite. 60The authors considered hydroxyapatite (Hap) concentration, temperature, time, pH, agitation speed, adsorbent dose and initial Pb(II) concentration as input model parameters and lead removal efficiency as model output response.ANFIS models the Pb adsorption process by combining fuzzy "if-then" logic with neural networks' superior learning capabilities (II).The anticipated model outcomes and the experimental ndings were remarkably consistent, with a correlation coefficient (R) close to unity and negligible model error.The ANFIS modelling results for metals remediation using various biomaterials have outperformed results obtained using standalone ANN frameworks and conventional statistical models. 52,84,91,129Despite its acceptance in many other elds, including, e.g.medicine, 130 energy, 131 sports 132 and passenger demand forecasting, 133 ANFIS suffers from the curse of dimensionality and computational cost.The complicated structure and gradient learning in ANFIS add to the computation cost of ANFIS.

Assessment of conventional, ANN and ensemble-ANN models
ANN is a data-driven modelling approach that addresses adsorption prediction and interpretation issues by employing dataset knowledge particular to an adsorbent-adsorbate combination.The standalone ANN frameworks extensively used Levenberg-Marquardt (LM) backpropagation training algorithm and hyperbolic tangent-linear activation functions to optimize the metal adsorption process on biomaterials systems (ESI, S2 †).The LM algorithm incorporates the fast convergence ability of the Gauss-Newton algorithm and inherits the steepest descent method's stability to minimize the modelling error. 134he role of activation function is critical in tuning the ANN model.The researchers have applied mainly hyperbolic tangent (tansig) activation function at the hidden layer as it centres each layer's output more or less around 0, which frequently aids in accelerating convergence. 135The current developments in the eld of machine learning demonstrate the potential of scaled exponential linear unit (SELU), rectied linear unit (ReLU) and exponential linear unit (ELU) to overcome the problems of overtting and huge training dataset. 136Since the experimental adsorption data set are not very big (<500 data points), scholars have usually selected classical activation functions for nonlinear mapping of data points.Future research can investigate the impact of varying dataset sizes, training algorithms, and activation functions on the quality of interactions and model performance.
The performance of standalone and ensembled ANN systems for simulating adsorptive eviction of metal ions using biomaterial adsorbents has also been studied along with traditional mathematical models (e.g.RSM, MLR, MNLR) as tabulated in Table 5.It was also reported that the ANN successfully optimized the metal adsorption process for datasets beyond the studied ranges. 48,57,62,98,99,137,138These results validate their true generalization capability.In the case of a smaller dataset (<50 data points), the results predicted by ANN models very well matched the actual data points, demonstrating the ANN's suitability to decrease reagent use, which would impact the economic aspect of wastewater treatment. 138,139The integration of evolutionary algorithms and fuzzy models with ANN has improved the predictive ability of ANN systems.This behaviour can be attributed to the knowledge of search algorithms to create multiple solutions to a given problem. 140Each solution holds various parameters that can aid in enhancing the ANN efficiency.Fig. 5 sums up the predictive power of ensemble ANNs over standalone frameworks and traditional statistical models.
The authors acknowledged the capacity of the developed ANN models with metaheuristic optimizers to simulate the adsorption of metal ions on biomaterials.Yet, there is a need to explore these optimizers with a varied dataset on different metal pollutants with a clear explanation of the methodological phase for developing the research knowledge and comparing their capacity to deal with the stochastic, nonlinear complex data.

Hybridized-ANN models
The process model development is an integral part of water treatment via adsorption.The classical means of modeling  adsorption include calculating parameters related to isotherm, kinetics and thermodynamics through experimental values obtained at optimum conditions.9][180][181] Considering the impact of individual variables, analytical error and uncertainty associated with the traditional experimental approach, different AI models are used to improve the mathematical representations of adsorption process models.In this regard, Rodríguez-Romero et al., 2020 hybridized the ANN with classical isotherm and kinetic equations to improve the arsenic adsorption capacity of carbonenriched biomaterial. 211The authors obtained the ANN-Langmuir model from the classical Langmuir functionality using initial metal concentration, pH and temperature as input parameters with sigmoid activation functions.Likewise, the other hybridized models were also obtained.The hybridized ANNs outperformed the traditional kinetics and isotherm models as portrayed in Fig. 6 where it is clear that the hybrid ANNs are less susceptible to error.
][184] ANN tools are easily used because they can establish dependencies and correlations between multiple variables.ANN architectures with equilibrium concentrations of metal toxins and temperature as net entrance data and metals adsorbed as the exit variables are processed to capture the best t for the single and multicomponent adsorption process. 53It is important to remark that similar ANN frameworks can be used to design multicomponent adsorption processes for metal removal at different operating conditions.The utility of AI has expanded with the hybridization of ANN with isotherm or kinetic equations to acquire pertinent adsorption parameters that are not possible using a standard model. 185part from isotherm and kinetics, estimating thermodynamic parameters of the adsorption process using ANN is an emerging eld of research.Recently, Zaferani et al., 2019 implemented ANN to recognize the standard Gibbs free energy changes (DG) related to Pb(II) adsorption process based on the changing temperature and initial metal concentration.The authors investigated different structures of ANN for modelling  DG and metal removal efficiency. 62The results revealed that the minimum value of DG (−6 kJ K −1 ) occurred at the highest temperature (55 °C) and the lowest initial Pb(II) concentration (10 ppm).The negative Gibbs free energy veried the spontaneity of the adsorption process.Limited studies explored the possibility of analyzing thermodynamics aspects of the adsorption process using ANN-framework.Much research is needed to create intelligent models that can predict the nature and viability of the adsorption process.
It should be emphasized that the parameters of conventional adsorption models are established by tting specic experimental data.This indicates that the parameters of conventional adsorption models are constant for a given range of experimental conditions (Tables 1-3).On the other hand, ANN model parameters are derived through concurrent regression of all experimental observations. 186Thus, hybrid adsorption model parameters are treated as nonlinear functions of the input variables used to train the articial neural network, enhancing their adaptability and data correlation capabilities.These results demonstrated that using ANNs to estimate analytical adsorption equations parameters signicantly improved modelling results.

Multicomponent adsorption
Wastewater is a matrix of multiple pollutants; therefore, developing a single technique for concurrent extraction of coexisting metallic impurities is critical.However, fabricating an adsorbent that considers the characteristics of all contaminants whose removal is required is challenging. 100,187The process of multiple metal adsorption on biomaterials is usually studied in the column set-up in the laboratory and analyzed using breakthrough curves; but the existence of various metal pollutants in the feed makes modeling of breakthrough curves complex due to the pollutants' antagonistic, synergistic, and noninteractive tendencies. 188Advanced models that illustrate multicomponent adsorption and the associated physics are part of the evolving research. 189In this context, for the rst time, Pauletto et al., 2020 implemented ANN with a Bayesian regularization algorithm to investigate the antagonistic and  synergistic effects during the adsorption of dye (MB) and metals (Co(II)), Ni(II)) in single, binary and ternary mixtures on ultrasound modied chitin. 212They optimized the input parameters (i.e.temperature and initial pollutants concentration) to simultaneously forecast the uptake capacity of individual adsorbates from a multicomponent system.The ANN-based simulations indicated that the optimized network of single component systems can be applied to model the equilibrium adsorption of cobalt (Co(II)), nickel (Ni(II), and methylene blue (MB) effectively (R 2 = 0.99) in multicomponent systems.
Simulating biomaterial systems for multi-metals adsorption is an emerging eld of study that has the potential to computationally design cost-effective adsorbents with tailored properties to effectively treat industrial effluents without the need for multiple stages involved in adsorption system design.Other advantages of this technique include cost reduction and time savings to generate high-efficiency adsorption systems that simultaneously treat diverse water pollutants.The future studies can analyse the application of ANN integrated with nature and human-inspired metaheuristic optimization algorithms for the adsorptive eviction of multiple species from BMs.

Sensitivity analysis
The ANN frameworks' limitations is their inability to comprehend the physico-chemistry behind the adsorption behaviour; therefore, their uninformed application to a sorption system without paying attention to the physicochemical characteristics could result in dubious outcomes.To address this concern, researchers used a sensitivity analysis of ANN to determine the impact of experimental factors on the adsorption of metal ions.A sensitivity analysis of the developed ANN allows assessment of the input attributes as per their impact on the output response.
In the literature, the Weights method has usually been employed to examine the sensitivity of the adsorption process and identify the most signicant parameters that inuence the adsorption performance (ANN output). 190The mathematical presentation of network weights for determining the relative weights of input parameters is given in ESI, Section S6. † In the biomaterial adsorption system, pH, initial concentration of adsorbate, and contact time were the most critical process variables that impacted the metal adsorption on biomaterials.Since the pH alters the ionic strength and affects the ionization of metals onto biomaterials, the contact time between adsorbate and adsorbent affects the available active sites, 213,214 whereas the concentration of metal affects the interaction of metal ions with the available binding sites.Furthermore, it was found that the quantity and quality of the biomaterial adsorbed signicantly impacted the effectiveness of the adsorption process. 73The medium of aqueous solutions also affected the adsorptive removal of metal ions.For example, the presence of organic matter and its derivatives or salinity might change the biomaterials' surface characteristics and block the metals' adsorption on biomaterials.Considering the wastewater treatment plants, the quantity of biomaterial required for successful adsorption of metal adsorbates at a xed initial concentration serves importance from an economic perspective.The process cost will be lowered when sufficient adsorption is attained with a small biomaterial dose.Since the selling cost of natural biomaterials is very low, but their excessive usage can increase their waste disposal costs, while inefficient use can increase the process cost.Thus, understanding how operating variables affect the adsorption using ANN approach will aid in the appropriate process design, scale-up and optimization of an industrial adsorption process.In addition, implementing neural networks will process monitoring and control, save time, and lower costs.
Besides determining the contribution of single input parameters, researchers studied the conjugate effects of multiple input parameters on ANN prediction.Fig. 7 shows the signicant decrement in the prediction error (MSE) for copper and mercury removal with the increasing combinations of input parameters.Fig. 7 shows that as the number of input variables in the group rose, the values of MSE decreased because of the strong effect of all parameters on adsorption capacity.Although the inuence of process variables has been explored widely, the contribution of biomaterial characteristics in terms of their lignin-cellulose-hemicellulose content, pore size distribution, particle size and surface area on the predictive ANN response has not been fully explored.The information about the inuence of the above-mentioned attributes can benet technologists and engineers in selecting and designing adsorption systems.
The sensitivity analysis was primarily reported in studies focusing on standalone ANN frameworks, which followed a gradient-based optimization scheme (details of studies in Table 5).Thus a comparative analysis of metaheuristic-based ensemble models and ANN can be carried out in future to predict the relative contribution of adsorption variables on the metal adsorption efficacy of BMs.Apart from Weights methods, there are other methods of calculating sensitivity and feature importance, e.g., partial derivate algorithm, 191 input perturbation algorithm, 192 prole 193 and stepwise method. 194There is a need to test the sensitivity of ANN response using different approaches to determine the optimal sensitivity criteria, which could be the focus of future studies.

Challenges and advancements in ANN technology for the removal of metals
The main disadvantage of ANN is its black box and empirical character.The connection link between neurons is denoted by weights, which are difficult to represent mathematically.The contribution of a specic input variable to the outcome of ANN is identied based on its numeric value and sign of the associated weight.The higher the weight value, the greater the independent variable's contribution to the expected response.The effects of negative weights on neurons are conicting.Thus, positive outcomes have a synergistic impact on the neurons, boosting the value of the response, whereas negative outcomes have the opposite effect and decrease the expected value of the output (Section 6).
Although the above-discussed sections demonstrate ANN as a superior approach to the traditional models due to less formal statistical training requirements, detection of complex nonlinear relationships and all possible interactions between the variables, there is a need to develop novel strategies that can provide in-depth analysis of adsorption phenomena in terms of surface interactions and associated adsorption energy.Recent research by Fagundez et al., 2021 offered novel hybrid ANN-isotherms for simultaneous estimation of isotherm and thermodynamics parameters to predict metal uptake capacity and associated thermodynamic parameters of various zeolites under different temperature conditions. 215The utility of molecular simulations combined with ANN has recently been reported as a valuable modelling strategy to gain insights into the mechanism of heavy metal adsorption on graphene nanocomposites with high accuracy. 195The computation models based on density functional theory (DFT) have been employed to determine the adsorption energies on solid surfaces.7][198][199] In addition to developing new computational strategies, the researchers emphasize on meaningful experimental results to understand the equilibrium, saturation and regenerative potential of adsorption systems from a chemical science point of view. 56,200he possibility of overtting is the second major issue that needs to be addressed by researchers while applying ANN algorithms to predict biomaterial systems' efficacy for wastewater treatments. 91,92To prevent the over-parameterization and over-training of the ANN system, researchers have advocated the implementation of emerging activation functions (e.g., SeLU, ReLU). 201,202Using simple models (e.g., AdaBoost) ensures the generalizability of output in the small dataset. 203t is commonly recognized that a smaller error value is better for optimum network learning; however, it may be possible that the network training stops due to getting stuck in local minima.Such situations call for hybridizing the ANN framework with novel evolutionary algorithms.Recently, Ke et al., 2021 proposed novel ANN-based-surrogate models (i.e., BA-ANN, SVM-ANN, RF-ANN, M5Tree-GP, M5Tree-ANN and GP-ANN) for predicting metal removal efficiency based on characteristics of carbonaceous materials, source of metal and environmental conditions. 107The particle swarm optimizer (PSO) has been coupled with ANN to predict the dye and copper removal efficiency using graphene oxide-based nanocomposites and pomelo-peel-based carbonaceous material. 204,205 Prospective scope ❖ Based on the reviewed literature on metal ion modelling using ANN, estimating the absorption capability of biomaterials other than polysaccharide-derived materials requires additional research.
❖ Models discussed were prepared and assessed based on metals present in synthetic solutions.The natural wastewater or water system is a complex matrix where various pollutants coexist.The inuence of co-existing metal pollutants in natural systems on the adsorption behaviour via ANN has not been fully explored.Thus, there is a greater scope of research in this domain.
❖ Although ANN-based models provided a better t than static adsorption models, the literature lacked sufficient research on the development of ANN systems that can best describe the breakthrough curves against dynamic adsorption models such as Thomas, Bohart-Adams and Yoon-Nelson models.Future research should demonstrate the performance of neural networks against dynamic adsorption models to forecast breakthroughs.
❖ As per the principles of circular economy, the reuse and recyclability of biomaterial systems are essential.A vast development of ANN models has predicted pollutant removal efficiency; however, little attention has yet been given to developing intelligent systems that can optimize the dose of eluting agents for maximum regeneration of adsorbent materials.Modelling desorption processes can allow further utilization and effective management of spent adsorbent materials.
❖ ANNs have been chiey applied to model the removal of heavy metals and dyes.But the potential of bioadsorbents to treat emerging contaminants such as per-and polyuoroalkyl substances (PFAS) and rare earth metals (e.g., neodymium, cerium, and lanthanum) via adsorption needs attention for advancements in adsorption systems design.
❖ Environmental remediation occurs in different climate conditions.Also, the wastewater being processed for reuse can be at varying temperatures.In such situations, modelling thermodynamic aspects of the adsorption process can give crucial information related to the efficacy of biomaterials and the feasibility of adsorption phenomena for a broad spectrum of temperatures.
❖ ANN results need to be compared with the latest machine learning models, which are not yet explored for simulating adsorption processes such as super learning, decision tree, deep learning, and data mining.These models have provided promising solutions for various problems related to environmental engineering; however, they are yet to be assessed for wastewater treatment applications.

Conclusion
Metal pollution treatment is essential to prevent waste metals' bioaccumulation, environmental pollution, and soil degradation.Biomaterials act as a versatile and cost-effective system for removing metals from wastewater.Different chemical and physical modication methods of natural biomaterials can improve their metal adsorption efficiency, but conventional laboratory-based research has yet to describe multicomponent adsorption systems comprehensively.An articial neural network can automate the adsorption process to optimize process variables and adsorbent fabrication pathways for increasing metal removal efficiency.Furthermore, ANN frameworks can generate hybrid isotherm and kinetic models that minimize error and accurately model an efficient, rapid, and cost-effective multicomponent system for metal removal.The application of ANN-based models leads to a better understanding of biomaterials' efficiency, energy, time and economic benets.The thermodynamic aspects of metal adsorption to improve environmental water quality and applications in water reuse is a burgeoning eld of research.The challenges of ANN can be briey summarized as a) collecting experimentally characterized data to lter and identify specic metal contaminants in the complex matrix of water; and b) establishing ensemble models to assist in solving local minima problems, thereby improving the prediction efficiency of ANN.The intervention of ANN demonstrated robustness and rigour in simulating adsorptive eviction of metal ions using BMs, which could be expanded for other organic and emergent pollutants.

Disclaimer
The research presented was not performed or funded by EPA and was not subject to EPA's quality system requirements.The views expressed in this article are those of the author(s) and do not necessarily represent the views or the policies of the US Environmental Protection Agency.

Fig. 2
Fig.2illustrates the ow chart for modelling the metal adsorption process via ANNs.Initially, the experimental Fig.1The dataset before analyzing and processing (the box plots generated using data listed in ESI, TablesS1 and S2†) *AD = adsorbent dose, IC = initial concentration, CT = contact time, T = temperature, PS = particle size, BD = bed depth, FR = flow rate, AS = agitation speed, MPE = metal pollutant efficiency, AC = adsorption capacity.*The middle line in the box represents the median, the center line represents the mean, while the bottom and top lines of the box represent the 1st and the 3rd quartiles, respectively.

R 2 R
The high R 2 (∼0.99) indicated the applicability of both the models in the prediction of the mercury removal using vibrio parahaemolyticus ANFIS predicted the maximum Pb(II) uptake with less than a 5% error deviation from the experimental values.In contrast, FFD showed a relatively weak prediction of biosorption capacityThe ANFIS architecture, aer 15 iterations, showed high R 2 between the predicted and experimental results of Cr(VI) and Cu(II) adsorption on the wheat straw with diminished root means square error values 80 ANFIS Contact time, nickel and cadmium ions concentration, adsorbent dose, pH, and particle size of adsorbent Removal efficiency R 2 , RMSE The results indicated a relatively more signicant inuence of pH and ion concentration on the Ni(II) and cadmium(II) removal efficiency using Typha domingensis 172 ANFIS Adsorbent weight, residence time, pH, and ion concentration Adsorption efficiency R 2 , RMSE The biomass dose and pH were depicted as the most inuential process parameters which affected the Cr(VI) sorption efficiency for date palm leaves and broad bean shoots, least training and checking error controlled the cadmium adsorption on rice straw, followed by the pH and adsorbent dose.The full factorial design also complemented the ANFIS The optimization results revealed the potential of ANN-GA (99.86%) to represent and explain actual Hg(II) adsorption data using yeast against the RSM (97.of 1.3% was found between the observed Cu(II) adsorption on banana oret and model results, which validated the ANN-GA hybrid structure.In addition, the pH and time have the most signicant inuence on the removal efficiency 72 FFNN model (trained with Bayesianregularization (BR) algorithm) and optimized with GWO efficiently modelled the adsorption of Pb(II) and Co(II) ions on Rafsanjan pistachio shell 101 ANN-COA Elution solvent, ow rate, the concentration of PAN [1-(2pyridylazo)-2-naphthol], adsorbent dose, pH, and volume of elution solvent Adsorption efficiency R 2 , RMSE The ANN-COA model predicted the output with a small residual error of 1.3% and R 2 value of 0.9954 for the uranium adsorption using zinc oxide nanoparticles-chitosan 177 a R 2 : coefficient of determination, MSE: mean square error, R: correlation coefficient, RMSE: root mean square error, AARE: absolute average relative error, SD: standard deviation, MRE: mean relative error, SSE: sum of square error, MAE: mean average error, ARE: average relative error, c 2 : chisquare, F obj : objective function, ARPE: average relative percentage error, RMS: root mean square.

Fig. 5
Fig. 5 Modelling error occurred in conventional, standalone and ensemble models for simulating adsorption on biomaterials (figure generated using the data from Section S5.6 †).

Fig. 7
Fig. 7 Influence of single and combinations of input variables on the ANN response.*AD = adsorbent dose, IC = initial metal ion concentration, T = temperature, CT = contact time and Sal.= salinity of aqueous medium.(A and B) were generated using the data obtained from ref. 168 with permission from [Elsevier], copyright [2019], while (C and D) were generated using the data obtained from ref. 77 with permission from [Springer Nature], copyright [2018].

Table 1
Time required (t e ) to reach equilibrium for the metal adsorption process using biomaterials a

Table 2
Model parameters of the adsorption isotherm used in the adsorption of specified metal contaminants onto the listed biomaterials adsorbents max (Mg g −1

Table 3
Details of nature of adsorption process at different temperature ranges

Table 4
Recently applied optimization methods in adsorptive removal of metals using biomaterials a 93 Cu(II), Pb(II), Zn(II), As(III), Cd(II), and Ni(II) a Least error from ANN-GA.

Table 5
Comparison of different reports on standalone and ensembled ANN-based modelling methods for adsorptive eviction of distinct metal ions using biomaterial adsorbents a MSEInitial concentration of adsorbate strongly affected the Cr(III) sorption efficiency, whereas treatment time inuenced the Cr(VI) sorption on nanocrystalline cellulose 70 ANN No. of adsorbents, adsorbent weights, pH, contact time, and ion concentration Sorption efficiency AARE, SD, MSE and R ANN results showed better predictive performance for all the biomaterials, namely, coconut shell, neem leaves, hyacinth toots, rice husk, rice bran, rice straw, neem bark, and sawdust of teakwood 146 ANN Residence time, ion concentration, adsorbent weight, pH and temperature Adsorption efficiency and nal pH R ANN response showed excellent agreement with the observed Ur (VI) adsorption results using polyacrylonitrile graed potato starch 79 ANN No. of adsorbents, time, ow rate, bed height, and initial concentration Removal efficiency AARE, SD, MSE and R ANN with a single hidden layer predicts Pb(II) sorption efficiency with reasonable accuracy on multiple biomaterials, i.e. coconut shells, neem leaves, hyacinth roots, and rice wastes 147 ANN pH, residence time, inoculum size and initial arsenic concentration Removal efficiency R 2 , MSE The distribution of model results closely tted the As(III) and As(V) experimental data points using algal biomass, i.e.Botryococcus braunii 148 ANN Adsorbent weight, pH, ion concentration, and residence time Removal efficiency R 2 ANN supplemented experimental results in a better explanation of Hg(II) adsorption on Sargassum bevanom biomass 149 ANN Adsorbent weight, residence time, and ion concentration Adsorption efficiency R 2 , MSE The excellent values of R 2 (>0.99) showed the precision of ANN in predicting the adsorption of Pb(II), Cd(II) and Ni(II) on

Table 5 (
Contd. ) 2 , MSE, SD The study found an enormous potential of ANN over the quadratic mathematical model (deviation ∼16.3%) to forecast Ni(II) adsorption on potamogeton pectinatus closer to the experimental response (R 2 = 0.9714, MSE = 1.4).Also, initial ion concentration has the highest and particle size has the most negligible inuence on removal efficiency ANN, RSM Metal concentration, pH, adsorbent weight, and temperature Removal efficiency R 2 The study reported that the ANN model (4-4-1) performed well (R 2 = 0.9971) for the Cr(VI) adsorption on cyanobacterial biomass with diminished error values against RSM ANN Adsorption dose, ion concentration and pH Removal efficiency R 2 The chromium adsorption on Borassus abellifer coir was modelled by ANN with a high coefficient of determination ANN, RSM Adsorption dose, ion concentration and pH Removal efficiency R 2 , RMSE The adsorptive removal of chromium using Flabellifer coir powder and Ragi husk powder was better simulated using the ANN scheme ANN, MLR Ion concentration, pH, residence time, and temperature Adsorption capacity R 2 , RMSE The dataset of chromium removal using maize bran was better modelled using the ANN framework ANN Adsorbent dosage, contact time, temperature, pH, metal ion concentration Removal efficiency R 2 , MSE An excellent t between ANN output and experimental results was achieved in 188 iterations for As(III) adsorption on Bacillus

Table 5 (
Contd. ) 2 , MSE The ANN displayed a compelling correlation between the predicted output and experimental response for cadmium adsorption on valonia tannin resin ANN, RSM Adsorbent weight, ion concentration and pH Adsorption capacity R 2 , MSE A high R 2 value conrmed the closeness between the predicted and observed values.The study reported the superiority of ANN over RSM in predicting Cu(II) adsorption capacity of ax meal ANN, RSM pH, temperature, residence time and ion concentration Adsorption capacity and removal efficiency R 2 , SSE and ARE ANN topology agreed excellently with the experimental data (R 2 ∼ 1) at low average relative errors of 1.032 and 0.