Recent advances in machine learning towards multiscale soft materials design

Modeling-driven materials by design for conjugated polymers: insights into optoelectronic, conformational, and thermomechanical properties

Conjugated polymers (CPs) have emerged as pivotal functional materials in the realm of flexible electronics and optoelectronic devices due to their unique blend of mechanical flexibility, solution processability, and tunable optoelectronic properties. This review synthesizes the latest molecular simulation-driven insights obtained from various multiscale modeling techniques, including quantum mechanics (QM), all-atomistic (AA) molecular dynamics (MD), coarse-grained (CG) modeling, and machine learning (ML), to elucidate the optoelectronic, structural, and thermomechanical properties of CPs. By integrating findings from our recent computational work with key experimental studies, we highlight the molecular mechanisms influencing the multifunctional performance of CPs. This comprehensive understanding aims to guide future research directions and applications in the modeling assisted design of high-performance CP-based materials and devices.

Surrogate Modeling of the Relative Entropy for Inverse Design Using Smolyak Sparse Grids

Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.

Computational Design of Peptides for Biomaterials Applications

Computer-aided molecular design and protein engineering emerge as promising and active subjects in bioengineering and biotechnological applications. On one hand, due to the advancing computing power in the past decade, modeling toolkits and force fields have been put to use for accurate multiscale modeling of biomolecules including lipid, protein, carbohydrate, and nucleic acids. On the other hand, machine learning emerges as a revolutionary data analysis tool that promises to leverage physicochemical properties and structural information obtained from modeling in order to build quantitative protein structure-function relationships. We review recent computational works that utilize state-of-the-art computational methods to engineer peptides and proteins for various emerging biomedical, antimicrobial, and antifreeze applications. We also discuss challenges and possible future directions toward developing a roadmap for efficient biomolecular design and engineering.

Data-Driven Design of Polymer-Based Biomaterials: High-throughput Simulation, Experimentation, and Machine Learning

Polymers, with the capacity to tunably alter properties and response based on manipulation of their chemical characteristics, are attractive components in biomaterials. Nevertheless, their potential as functional materials is also inhibited by their complexity, which complicates rational or brute-force design and realization. In recent years, machine learning has emerged as a useful tool for facilitating materials design via efficient modeling of structure-property relationships in the chemical domain of interest. In this Spotlight, we discuss the emergence of data-driven design of polymers that can be deployed in biomaterials with particular emphasis on complex copolymer systems. We outline recent developments, as well as our own contributions and takeaways, related to high-throughput data generation for polymer systems, methods for surrogate modeling by machine learning, and paradigms for property optimization and design. Throughout this discussion, we highlight key aspects of successful strategies and other considerations that will be relevant to the future design of polymer-based biomaterials with target properties.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Current Advancement and Future Prospects: Biomedical Nanoengineering

Recent advancements in biomedicine have seen a significant reliance on nanoengineering, as traditional methods often fall short in harnessing the unique attributes of biomaterials. Nanoengineering has emerged as a valuable approach to enhance and enrich the performance and functionalities of biomaterials, driving research and development in the field. This review emphasizes the most prevalent biomaterials used in biomedicine, including polymers, nanocomposites, and metallic materials, and explores the pivotal role of nanoengineering in developing biomedical treatments and processes. Particularly, the review highlights research focused on gaining an in-depth understanding of material properties and effectively enhancing material performance through molecular dynamics simulations, all from a nanoengineering perspective.

Dissociation cross sections and rates in O2 + N collisions: molecular dynamics simulations combined with machine learning

The collision-induced dissociation reaction of O2 (v, j) + N, a fundamental process in nonequilibrium air flows around reentry vehicles, has been studied systematically by applying molecular dynamics simulations on the 2A', 4A' and 6A' potential energy surfaces of NO2 in a wide temperature range. In particular, we have directly investigated the role of the 6A' surface in this process and discussed the applicability of the simplified approximate rate models proposed by Esposito et al. and Andrienko et al. based on the lowest two surfaces. The present work indicates that the state-selected dissociation of O2 + N is dominated by the 6A' surface for all except for the low-lying O2 states. Furthermore, a complete database of rovibrationally detailed cross sections and rate coefficients is a prerequisite for modeling the relevant nonequilibrium air flows in spacecraft reentry. Here, the combination of the quasi-classical trajectory (QCT) and the neural network (NN) has been proposed to predict all state-selected dissociation cross sections and further construct dissociation parameter sets. All NN-based models established in this work accurately reproduce the results calculated from QCT simulations over a wide range of rovibrational quantum numbers with R2 > 0.99. Compared with the explicit QCT simulations, the computational requirement for predicting cross sections and rates based on the NN models significantly reduces. Finally, thermal equilibrium rate coefficients computed from NN models match remarkably well the available theoretical and experimental results in the whole temperature range explored.

Developing efficient deep learning model for predicting copolymer properties

Deep learning models are gaining popularity and potency in predicting polymer properties. These models can be built using pre-existing data and are useful for the rapid prediction of polymer properties. However, the performance of a deep learning model is intricately connected to its topology and the volume of training data. There is no facile protocol available to select a deep learning architecture, and there is a lack of a large volume of homogeneous sequence-property data of polymers. These two factors are the primary bottleneck for the efficient development of deep learning models for polymers. Here we assess the severity of these factors and propose strategies to address them. We show that a linear layer-by-layer expansion of a neural network can help in identifying the best neural network topology for a given problem. Moreover, we map the discrete sequence space of a polymer to a continuous one-dimensional latent space using a feature extraction technique to identify minimal data points for training a deep learning model. We implement these approaches for two representative cases of building sequence-property surrogate models, viz., the single-molecule radius of gyration of a copolymer and copolymer compatibilizer. This work demonstrates efficient methods for building deep learning models with minimal data and hyperparameters for predicting sequence-defined properties of polymers.

Machine learning approaches for the optimization of packing densities in granular matter

The fundamental question of how densely granular matter can pack and how this density depends on the shape of the constituent particles has been a longstanding scientific problem. Previous work has mainly focused on empirical approaches based on simulations or mean-field theory to investigate the effect of shape variation on the resulting packing densities, focusing on a small set of pre-defined shapes like dimers, ellipsoids, and spherocylinders. Here we discuss how machine learning methods can support the search for optimally dense packing shapes in a high-dimensional shape space. We apply dimensional reduction and regression techniques based on random forests and neural networks to find novel dense packing shapes by numerical optimization. Moreover, an investigation of the regression function in the dimensionally reduced shape representation allows us to identify directions in the packing density landscape that lead to a strongly non-monotonic variation of the packing density. The predictions obtained by machine learning are compared with packing simulations. Our approach can be more widely applied to optimize the properties of granular matter by varying the shape of its constituent particles.

Unleashing the Power of Artificial Intelligence in Materials Design

The integration of artificial intelligence (AI) algorithms in materials design is revolutionizing the field of materials engineering thanks to their power to predict material properties, design de novo materials with enhanced features, and discover new mechanisms beyond intuition. In addition, they can be used to infer complex design principles and identify high-quality candidates more rapidly than trial-and-error experimentation. From this perspective, herein we describe how these tools can enable the acceleration and enrichment of each stage of the discovery cycle of novel materials with optimized properties. We begin by outlining the state-of-the-art AI models in materials design, including machine learning (ML), deep learning, and materials informatics tools. These methodologies enable the extraction of meaningful information from vast amounts of data, enabling researchers to uncover complex correlations and patterns within material properties, structures, and compositions. Next, a comprehensive overview of AI-driven materials design is provided and its potential future prospects are highlighted. By leveraging such AI algorithms, researchers can efficiently search and analyze databases containing a wide range of material properties, enabling the identification of promising candidates for specific applications. This capability has profound implications across various industries, from drug development to energy storage, where materials performance is crucial. Ultimately, AI-based approaches are poised to revolutionize our understanding and design of materials, ushering in a new era of accelerated innovation and advancement.

Transfer Learning of Full Molecular Weight Distributions via High-Throughput Computer-Controlled Polymerization

The skew and shape of the molecular weight distribution (MWD) of polymers have a significant impact on polymer physical properties. Standard summary metrics statistically derived from the MWD only provide an incomplete picture of the polymer MWD. Machine learning (ML) methods coupled with high-throughput experimentation (HTE) could potentially allow for the prediction of the entire polymer MWD without information loss. In our work, we demonstrate a computer-controlled HTE platform that is able to run up to 8 unique variable conditions in parallel for the free radical polymerization of styrene. The segmented-flow HTE system was equipped with an inline Raman spectrometer and offline size exclusion chromatography (SEC) to obtain time-dependent conversion and MWD, respectively. Using ML forward models, we first predict monomer conversion, intrinsically learning varying polymerization kinetics that change for each experimental condition. In addition, we predict entire MWDs including the skew and shape as well as SHAP analysis to interpret the dependence on reagent concentrations and reaction time. We then used a transfer learning approach to use the data from our high-throughput flow reactor to predict batch polymerization MWDs with only three additional data points. Overall, we demonstrate that the combination of HTE and ML provides a high level of predictive accuracy in determining polymerization outcomes. Transfer learning can allow exploration outside existing parameter spaces efficiently, providing polymer chemists with the ability to target the synthesis of polymers with desired properties.

Sequence Patterning, Morphology, and Dispersity in Single-Chain Nanoparticles: Insights from Simulation and Machine Learning

Single-chain nanoparticles (SCNPs) are intriguing materials inspired by proteins that consist of a single precursor polymer chain that has collapsed into a stable structure. In many prospective applications, such as catalysis, the utility of a single-chain nanoparticle will intricately depend on the formation of a mostly specific structure or morphology. However, it is not generally well understood how to reliably control the morphology of single-chain nanoparticles. To address this knowledge gap, we simulate the formation of 7680 distinct single-chain nanoparticles from precursor chains that span a wide range of, in principle, tunable patterning characteristics of cross-linking moieties. Using a combination of molecular simulation and machine learning analyses, we show how the overall fraction of functionalization and blockiness of cross-linking moieties biases the formation of certain local and global morphological characteristics. Importantly, we illustrate and quantify the dispersity of morphologies that arise due to the stochastic nature of collapse from a well-defined sequence as well as from the ensemble of sequences that correspond to a given specification of precursor parameters. Moreover, we also examine the efficacy of precise sequence control in achieving morphological outcomes in different regimes of precursor parameters. Overall, this work critically assesses how precursor chains might be feasibly tailored to achieve given SCNP morphologies and provides a platform to pursue future sequence-based design.

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

Learning to self-fold at a bifurcation

Disordered mechanical systems can deform along a network of pathways that branch and recombine at special configurations called bifurcation points. Multiple pathways are accessible from these bifurcation points; consequently, computer-aided design algorithms have been sought to achieve a specific structure of pathways at bifurcations by rationally designing the geometry and material properties of these systems. Here, we explore an alternative physical training framework in which the topology of folding pathways in a disordered sheet is changed in a desired manner due to changes in crease stiffnesses induced by prior folding. We study the quality and robustness of such training for different "learning rules," that is, different quantitative ways in which local strain changes the local folding stiffness. We experimentally demonstrate these ideas using sheets with epoxy-filled creases whose stiffnesses change due to folding before the epoxy sets. Our work shows how specific forms of plasticity in materials enable them to learn nonlinear behaviors through their prior deformation history in a robust manner.

Machine learning enabled quantification of the hydrogen bonds inside the polyelectrolyte brush layer probed using all-atom molecular dynamics simulations

The configuration of densely grafted charged polyelectrolyte (PE) brushes is strongly dictated by the properties and behavior of the counterions that screen the PE brush charges and the solvent molecules (typically water) that solvate the brush molecules and these screening counterions. Only recently, efforts have been made to study the PE brushes atomistically, thereby shedding light on the properties of brush-supported ions and water molecules. However, even for such efforts, there are limitations associated with using a generic definition to estimate certain properties of water and ions inside the brush layer. For example, water-water hydrogen bonds (HBs) will behave differently for locations outside and inside the brush layer, given the fact that the densely closely grafted PE brush molecules create a soft nanoconfinement where the water connectivity becomes highly disrupted: therefore, using the same definition to quantify the HBs inside and outside the brush layer will be unwise. In this paper, we address this limitation by employing an unsupervised machine learning (ML) approach to predict the water-water hydrogen bonding inside a cationic PE brush layer modeled using all-atom molecular dynamics (MD) simulations. The ML method, which relies on a clustering approach and uses the equilibrium coordinates of the water molecules (obtained from the all-atom MD simulations) as the input, is capable of identifying the structural modification of water-water HBs (revealed through appropriate clustering of the data) inside the PE brush layer induced soft nanoconfinement. Such capabilities would not have been possible by using a generic definition of the HBs. Our calculations lead to four key findings: (1) the clusters formed inside and outside the brush layer are structurally similar; (2) the margin of the cluster is shorter inside the PE brush layer confirming the possible disruption of the HBs inside the PE brush layer; (3) the average "hydrogen-acceptor-oxygen-donor-oxygen" angle that defines the HB is reduced for the HBs formed inside the brush layer; (4) the use of the generic definition (definition usable for characterizing the HBs in brush-free bulk) leads to an overprediction of the number of HBs formed inside the PE brush layer.

Regression analysis for predicting the elasticity of liquid crystal elastomers

It is highly desirable but difficult to understand how microscopic molecular details influence the macroscopic material properties, especially for soft materials with complex molecular architectures. In this study we focus on liquid crystal elastomers (LCEs) and aim at identifying the design variables of their molecular architectures that govern their macroscopic deformations. We apply the regression analysis using machine learning (ML) to a database containing the results of coarse grained molecular dynamics simulations of LCEs with various molecular architectures. The predictive performance of a surrogate model generated by the regression analysis is also tested. The database contains design variables for LCE molecular architectures, system and simulation conditions, and stress-strain curves for each LCE molecular system. Regression analysis is applied using the stress-strain curves as objective variables and the other factors as explanatory variables. The results reveal several descriptors governing the stress-strain curves. To test the predictive performance of the surrogate model, stress-strain curves are predicted for LCE molecular architectures that were not used in the ML scheme. The predicted curves capture the characteristics of the results obtained from molecular dynamics simulations. Therefore, the ML scheme has great potential to accelerate LCE material exploration by detecting the key design variables in the molecular architecture and predicting the LCE deformations.

An automated biomateriomics platform for sustainable programmable materials discovery

Recently, the potential to create functional materials from various forms of organic matter has received increased interest due to its potential to address environmental concerns. However, the process of creating novel materials from biomass requires extensive experimentation. A promising means of predicting the properties of such materials would be the use of machine-learning models trained on or integrated into self-learned experimental data and methods. We outline an automated system for the discovery and characterization of novel, sustainable, and functional materials from input biomass. Artificial intelligence provides the capacity to examine experimental data, draw connections between composite composition and behavior, and design future experiments to expand the system's understanding of the studied materials. Extensions to the system are described that could further accelerate the discovery of sustainable composites, including the use of interpretable machine-learning methods to expand the insights gleaned from to human-readable materiomic insights about material process-structure-functional relationships.

Leveraging Theory for Enhanced Machine Learning

The application of machine learning to the materials domain has traditionally struggled with two major challenges: a lack of large, curated data sets and the need to understand the physics behind the machine-learning prediction. The former problem is particularly acute in the polymers domain. Here we aim to simultaneously tackle these challenges through the incorporation of scientific knowledge, thus, providing improved predictions for smaller data sets, both under interpolation and extrapolation, and a degree of explainability. We focus on imperfect theories, as they are often readily available and easier to interpret. Using a system of a polymer in different solvent qualities, we explore numerous methods for incorporating theory into machine learning using different machine-learning models, including Gaussian process regression. Ultimately, we find that encoding the functional form of the theory performs best followed by an encoding of the numeric values of the theory.

Machine Learning for Property Prediction and Optimization of Polymeric Nanocomposites: A State-of-the-Art

Recently, the field of polymer nanocomposites has been an area of high scientific and industrial attention due to noteworthy improvements attained in these materials, arising from the synergetic combination of properties of a polymeric matrix and an organic or inorganic nanomaterial. The enhanced performance of those materials typically involves superior mechanical strength, toughness and stiffness, electrical and thermal conductivity, better flame retardancy and a higher barrier to moisture and gases. Nanocomposites can also display unique design possibilities, which provide exceptional advantages in developing multifunctional materials with desired properties for specific applications. On the other hand, machine learning (ML) has been recognized as a powerful predictive tool for data-driven multi-physical modelling, leading to unprecedented insights and an exploration of the system's properties beyond the capability of traditional computational and experimental analyses. This article aims to provide a brief overview of the most important findings related to the application of ML for the rational design of polymeric nanocomposites. Prediction, optimization, feature identification and uncertainty quantification are presented along with different ML algorithms used in the field of polymeric nanocomposites for property prediction, and selected examples are discussed. Finally, conclusions and future perspectives are highlighted.

Versatilely Manipulating the Mechanical Properties of Polymer Nanocomposites by Incorporating Porous Fillers: A Molecular Dynamics Simulation Study

Polymer nanocomposites (PNCs) have been attracting myriad scientific and technological attention due to their promising mechanical and functional properties. However, there remains a need for an efficient method that can further strengthen the mechanical performance of PNCs. Here, we propose a strategy to design and fabricate novel PNCs by incorporating porous fillers (PFs) such as metal-organic frameworks with ultrahigh specific surface areas and tunable nanospaces to polymer matrices via coarse-grained molecular dynamics simulations. Three important parameters─the polymer chain stiffness (k), the interaction strength between the PF center and the end functional groups of polymer chains (ε_center end), and the PF weight fraction (w)─are systematically examined. First, attributed to the penetration of polymer chains into PFs at a strong ε_center end, the dimension of polymer chains such as the radius of gyration and the end-to-end distance increases greatly as a function of k compared to the case of the neat polymer system. The penetration of polymer chains is validated by characterizing the radial distribution function between end functional groups and filler centers, as well as the visualization of the snapshots. Also, the dispersion state of PFs tends to be good because of the chain penetration. Then, the glass transition temperature ratio of PNCs to that of the neat systems exhibits a maximum in the case of k = 5ε, indicating that the strongest interlocking between polymer chains and PFs occurs at intermediate chain stiffness. The polymer chain dynamics of PNCs decreases to a plateau at k = 5ε and then becomes stable, and the relative mobility to that of the neat system as well presents the same variation trend. Furthermore, the mechanical property under uniaxial deformation is thoroughly studied, and intermediates k, ε_center end, and w can bring about the best mechanical property. This is because of the robust penetration and interaction, which is confirmed by calculating the stress of every component of PNCs with and without end functional groups and PF centers as well as the nonbonded interaction energy change between different components. Finally, the optimal condition (k = 5.36ε, ε_center end = 5.29ε, and w = 6.54%) to design the PNC with superior mechanical behavior is predicted by Gaussian process regression, an active machine learning (ML) method. Overall, incorporating PFs greatly enhances the entanglements and interactions between polymer chains and nanofillers and brings effective mechanical reinforcements with lower filler weight fractions. We anticipate that this will provide new routes to the design of mechanically reinforced PNCs.

Molecular Modeling in Anion Exchange Membrane Research: A Brief Review of Recent Applications

Anion Exchange Membrane (AEM) fuel cells have attracted growing interest, due to their encouraging advantages, including high power density and relatively low cost. AEM is a polymer matrix, which conducts hydroxide (OH-) ions, prevents physical contact of electrodes, and has positively charged head groups (mainly quaternary ammonium (QA) groups), covalently bound to the polymer backbone. The chemical instability of the quaternary ammonium (QA)-based head groups, at alkaline pH and elevated temperature, is a significant threshold in AEMFC technology. This review work aims to introduce recent studies on the chemical stability of various QA-based head groups and transportation of OH- ions in AEMFC, via modeling and simulation techniques, at different scales. It starts by introducing the fundamental theories behind AEM-based fuel-cell technology. In the main body of this review, we present selected computational studies that deal with the effects of various parameters on AEMs, via a variety of multi-length and multi-time-scale modeling and simulation methods. Such methods include electronic structure calculations via the quantum Density Functional Theory (DFT), ab initio, classical all-atom Molecular Dynamics (MD) simulations, and coarse-grained MD simulations. The explored processing and structural parameters include temperature, hydration levels, several QA-based head groups, various types of QA-based head groups and backbones, etc. Nowadays, many methods and software packages for molecular and materials modeling are available. Applications of such methods may help to understand the transportation mechanisms of OH- ions, the chemical stability of functional head groups, and many other relevant properties, leading to a performance-based molecular and structure design as well as, ultimately, improved AEM-based fuel cell performances. This contribution aims to introduce those molecular modeling methods and their recent applications to the AEM-based fuel cells research community.

Predicting Young's Modulus of Linear Polyurethane and Polyurethane-Polyurea Elastomers: Bridging Length Scales with Physicochemical Modeling and Machine Learning

Predicting the properties of complex polymeric materials based on monomer chemistry requires modeling physical interactions that bridge molecular, interchain, microstructure, and bulk length scales. For polyurethanes, a polymer class with global commercial and industrial significance, these multiscale challenges are intrinsic due to the thermodynamic incompatibility of the urethane and polyol-rich domains, resulting in heterogeneities from molecular to microstructural length scales. Machine learning can model patterns in data to establish a relationship between the monomer chemistry and bulk material properties, but this is made difficult by small data sets and a diverse set of monomers. Using a data set of 63 industrially relevant and complex elastomers, we demonstrate that accurate machine learning predictions are possible when monomer chemistry is used to estimate interactions at interchain length scales. Here, these features were used to accurately (r² = 0.91) predict the Young's modulus of polyurethane and polyurethane-urea elastomers. Furthermore, by a query of the trained model for compositions that yield a target modulus within the range of accessible values, the capabilities of using this methodology as a design tool are demonstrated. The presented methodology could become increasingly useful in building models for materials with small data sets and may guide the interpretation of the underlying physicochemical forces.

FAIR data enabling new horizons for materials research

The prosperity and lifestyle of our society are very much governed by achievements in condensed matter physics, chemistry and materials science, because new products for sectors such as energy, the environment, health, mobility and information technology (IT) rely largely on improved or even new materials. Examples include solid-state lighting, touchscreens, batteries, implants, drug delivery and many more. The enormous amount of research data produced every day in these fields represents a gold mine of the twenty-first century. This gold mine is, however, of little value if these data are not comprehensively characterized and made available. How can we refine this feedstock; that is, turn data into knowledge and value? For this, a FAIR (findable, accessible, interoperable and reusable) data infrastructure is a must. Only then can data be readily shared and explored using data analytics and artificial intelligence (AI) methods. Making data 'findable and AI ready' (a forward-looking interpretation of the acronym) will change the way in which science is carried out today. In this Perspective, we discuss how we can prepare to make this happen for the field of materials science.

Machine Learning-Assisted Design of Material Properties

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical, inverse methods that frame design as a constrained optimization problem present an attractive alternative. However, even efficient algorithms require time- and resource-intensive characterization of material properties many times during optimization, imposing a design bottleneck. Approaches that incorporate machine learning can help address this limitation and accelerate the discovery of materials with targeted properties. In this article, we review how to leverage machine learning to reduce dimensionality in order to effectively explore design space, accelerate property evaluation, and generate unconventional material structures with optimal properties. We also discuss promising future directions, including integration of machine learning into multiple stages of a design algorithm and interpretation of machine learning models to understand how design parameters relate to material properties. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics-polymeric configuration characterization, feed-forward property prediction, and inverse design-in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

Data-Driven Methods for Accelerating Polymer Design

Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.

Random Forest Predictor for Diblock Copolymer Phase Behavior

Physics-based models are the primary approach for modeling the phase behavior of block copolymers. However, the successful use of self-consistent field theory (SCFT) for designing new materials relies on the correct chemistry- and temperature-dependent Flory-Huggins interaction parameter χ_AB that quantifies the incompatibility between the two blocks A and B as well as accurate estimation of the ratio of Kuhn lengths (b_A/b_B) and block densities. This work uses machine learning to model the phase behavior of AB diblock copolymers by using the chemical identities of blocks directly, obviating the need for measurement of χ_AB and b_A/b_B. The random forest approach employed predicts the phase behavior with almost 90% accuracy after training on a data set of 4768 data points, almost twice the accuracy obtained using SCFT employing χ_AB from group contribution theory. The machine-learning model is notably sensitive toward the uncertainty in measuring molecular parameters; however, its accuracy still remains at least 60% even for highly uncertain experimental measurements. Accuracy is substantially reduced when extrapolating to chemistries outside the training set. This work demonstrates that a random forest phase predictor performs remarkably well in many scenarios, providing an opportunity to predict self-assembly without measurement of molecular parameters.

Machine-Learning-Guided Discovery of 19F MRI Agents Enabled by Automated Copolymer Synthesis

Modern polymer science suffers from the curse of multidimensionality. The large chemical space imposed by including combinations of monomers into a statistical copolymer overwhelms polymer synthesis and characterization technology and limits the ability to systematically study structure-property relationships. To tackle this challenge in the context of 19F magnetic resonance imaging (MRI) agents, we pursued a computer-guided materials discovery approach that combines synergistic innovations in automated flow synthesis and machine learning (ML) method development. A software-controlled, continuous polymer synthesis platform was developed to enable iterative experimental-computational cycles that resulted in the synthesis of 397 unique copolymer compositions within a six-variable compositional space. The nonintuitive design criteria identified by ML, which were accomplished by exploring <0.9% of the overall compositional space, lead to the identification of >10 copolymer compositions that outperformed state-of-the-art materials.

The Middle Science: Traversing Scale In Complex Many-Body Systems

A roadmap is developed that integrates simulation methodology and data science methods to target new theories that traverse the multiple length- and time-scale features of many-body phenomena.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Topics in the mathematical design of materials

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Deep Learning of Binary Solution Phase Behavior of Polystyrene

Predicting binary solution phase behavior of polymers has remained a challenge since the early theory of Flory-Huggins, hindering the processing, synthesis, and design of polymeric materials. Herein, we take a complementary data-driven approach by building a machine learning framework to make fast and accurate predictions of polymer solution cloud point temperatures. Using polystyrene, both upper and lower critical solution temperatures are predicted within experimental uncertainty (1-2 °C) with a deep neural network, Gaussian process regression (GPR) model, and a combination of polymer, solvent, and state features. The GPR model also enables intelligent exploration of solution phase space, where as little as 25 cloud points are required to make predictions within 2 °C for polystyrene of arbitrary molecular weight in cyclohexane. This study demonstrates the effectiveness of machine learning for the prediction of liquid-liquid equilibrium of polymer solutions and establishes a framework to incorporate other polymers and complex macromolecular architectures.

Deep learning-based estimation of Flory-Huggins parameter of A-B block copolymers from cross-sectional images of phase-separated structures

In this study, deep learning (DL)-based estimation of the Flory-Huggins χ parameter of A-B diblock copolymers from two-dimensional cross-sectional images of three-dimensional (3D) phase-separated structures were investigated. 3D structures with random networks of phase-separated domains were generated from real-space self-consistent field simulations in the 25-40 χN range for chain lengths (N) of 20 and 40. To confirm that the prepared data can be discriminated using DL, image classification was performed using the VGG-16 network. We comprehensively investigated the performances of the learned networks in the regression problem. The generalization ability was evaluated from independent images with the unlearned χN. We found that, except for large χN values, the standard deviation values were approximately 0.1 and 0.5 for A-component fractions of 0.2 and 0.35, respectively. The images for larger χN values were more difficult to distinguish. In addition, the learning performances for the 4-class problem were comparable to those for the 8-class problem, except when the χN values were large. This information is useful for the analysis of real experimental image data, where the variation of samples is limited.

Sequence-Engineering Polyethylene-Polypropylene Copolymers with High Thermal Conductivity Using a Molecular-Dynamics-Based Genetic Algorithm

Polymer sequence engineering is emerging as a potential tool to modulate material properties. Here, we employ a combination of a genetic algorithm (GA) and atomistic molecular dynamics (MD) simulation to design polyethylene-polypropylene (PE-PP) copolymers with the aim of identifying a specific sequence with high thermal conductivity. PE-PP copolymers with various sequences at the same monomer ratio are found to have a broad distribution of thermal conductivities. This indicates that the monomer sequence has a crucial effect on thermal energy transport of the copolymers. A non-periodic and non-intuitive optimal sequence is indeed identified by the GA, which gives the highest thermal conductivity compared with any regular block copolymers, for example, diblock, triblock, and hexablock. In comparison to the bulk density, chain conformations, and vibrational density of states, the monomer sequence has the strongest impact on the efficiency of thermal energy transport via inter- and intra-molecular interactions. Our work highlights polymer sequence engineering as a promising approach for tuning the thermal conductivity of copolymers, and it provides an example application of integrating atomistic MD modeling with the GA for computational material design.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

Characterising soft matter using machine learning

Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.

Bias free multiobjective active learning for materials design and discovery

The design rules for materials are clear for applications with a single objective. For most applications, however, there are often multiple, sometimes competing objectives where there is no single best material and the design rules change to finding the set of Pareto optimal materials. In this work, we leverage an active learning algorithm that directly uses the Pareto dominance relation to compute the set of Pareto optimal materials with desirable accuracy. We apply our algorithm to de novo polymer design with a prohibitively large search space. Using molecular simulations, we compute key descriptors for dispersant applications and drastically reduce the number of materials that need to be evaluated to reconstruct the Pareto front with a desired confidence. This work showcases how simulation and machine learning techniques can be coupled to discover materials within a design space that would be intractable using conventional screening approaches.

Enabling Circular Economy: The Overlooked Role of Inorganic Materials Chemistry

Circular economy is considered a new chance to build a more sustainable world from both the social and the economic point of view. In this Essay, the possible contribution of inorganic chemistry towards a smooth transition to circularity in inorganic materials design and production is discussed by adopting an interdisciplinary approach.

Automation and data-driven design of polymer therapeutics

Polymers are uniquely suited for drug delivery and biomaterial applications due to tunable structural parameters such as length, composition, architecture, and valency. To facilitate designs, researchers may explore combinatorial libraries in a high throughput fashion to correlate structure to function. However, traditional polymerization reactions including controlled living radical polymerization (CLRP) and ring-opening polymerization (ROP) require inert reaction conditions and extensive expertise to implement. With the advent of air-tolerance and automation, several polymerization techniques are now compatible with well plates and can be carried out at the benchtop, making high throughput synthesis and high throughput screening (HTS) possible. To avoid HTS pitfalls often described as "fishing expeditions," it is crucial to employ intelligent and big data approaches to maximize experimental efficiency. This is where the disruptive technologies of machine learning (ML) and artificial intelligence (AI) will likely play a role. In fact, ML and AI are already impacting small molecule drug discovery and showing signs of emerging in drug delivery. In this review, we present state-of-the-art research in drug delivery, gene delivery, antimicrobial polymers, and bioactive polymers alongside data-driven developments in drug design and organic synthesis. From this insight, important lessons are revealed for the polymer therapeutics community including the value of a closed loop design-build-test-learn workflow. This is an exciting time as researchers will gain the ability to fully explore the polymer structural landscape and establish quantitative structure-property relationships (QSPRs) with biological significance.

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.

Inverse design of nonequilibrium steady states: A large-deviation approach

The design of small scale nonequilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for nonequilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large-deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large-deviation functional for the empirical density and flow, and a "relaxation" algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking.

Accelerating copolymer inverse design using monte carlo tree search

There exists a broad class of sequencing problems in soft materials such as proteins and polymers that can be formulated as a heuristic search that involves decision making akin to a computer game. AI gaming algorithms such as Monte Carlo tree search (MCTS) gained prominence after their exemplary performance in the computer Go game and are decision trees aimed at identifying the path (moves) that should be taken by the policy to reach the final winning or optimal solution. Major challenges in inverse sequencing problems are that the materials search space is extremely vast and property evaluation for each sequence is computationally demanding. Reaching an optimal solution by minimizing the total number of evaluations in a given design cycle is therefore highly desirable. We demonstrate that one can adopt this approach for solving the sequencing problem by developing and growing a decision tree, where each node in the tree is a candidate sequence whose fitness is directly evaluated by molecular simulations. We interface MCTS with MD simulations and use a representative example of designing a copolymer compatibilizer, where the goal is to identify sequence specific copolymers that lead to zero interfacial energy between two immiscible homopolymers. We apply the MCTS algorithm to polymer chain lengths varying from 10-mer to 30-mer, wherein the overall search space varies from 210 (1024) to 230 (∼1 billion). In each case, we identify a target sequence that leads to zero interfacial energy within a few hundred evaluations demonstrating the scalability and efficiency of MCTS in exploring practical materials design problems with exceedingly vast chemical/material search space. Our MCTS-MD framework can be easily extended to several other polymer and protein inverse design problems, in particular, for cases where sequence-property data is either unavailable and/or is resource intensive.