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Abstract Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models’ predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design. 

Abstract Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big data sets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent-variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable data sets. By extending variational inference to LVGP models, the large training data set is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large data sets with over 104 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of categorical factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials. 

Organic molecules and polymers have a broad range of applications in biomedical, chemical, and materials science fields. Traditional design approaches for organic molecules and polymers are mainly experimentally-driven, guided by experience, intuition, and conceptual insights. Though they have been successfully applied to discover many important materials, these methods are facing significant challenges due to the tremendous demand of new materials and vast design space of organic molecules and polymers. Accelerated and inverse materials design is an ideal solution to these challenges. With advancements in high-throughput computation, artificial intelligence (especially machining learning, ML), and the growth of materials databases, ML-assisted materials design is emerging as a promising tool to flourish breakthroughs in many areas of materials science and engineering. To date, using ML-assisted approaches, the quantitative structure property/activity relation for material property prediction can be established more accurately and efficiently. In addition, materials design can be revolutionized and accelerated much faster than ever, through ML-enabled molecular generation and inverse molecular design. In this perspective, we review the recent progresses in ML-guided design of organic molecules and polymers, highlight several successful examples, and examine future opportunities in biomedical, chemical, and materials science fields. We further discuss the relevant challenges to solve in order to fully realize the potential of ML-assisted materials design for organic molecules and polymers. In particular, this study summarizes publicly available materials databases, feature representations for organic molecules, open-source tools for feature generation, methods for molecular generation, and ML models for prediction of material properties, which serve as a tutorial for researchers who have little experience with ML before and want to apply ML for various applications. Last but not least, it draws insights into the current limitations of ML-guided design of organic molecules and polymers. We anticipate that ML-assisted materials design for organic molecules and polymers will be the driving force in the near future, to meet the tremendous demand of new materials with tailored properties in different fields. 

Data-driven methods have attracted increasingly more attention in materials research since the advent of the material genome initiative. The combination of materials science with computer science, statistics, and data-driven methods aims to expediate materials research and applications and can utilize both new and archived research data. In this paper, we present a data driven and deep learning approach that builds a portion of the structure–property relationship for polymer nanocomposites. Analysis of archived experimental data motivates development of a computational model which allows demonstration of the approach and gives flexibility to sufficiently explore a wide range of structures. Taking advantage of microstructure reconstruction methods and finite element simulations, we first explore qualitative relationships between microstructure descriptors and mechanical properties, resulting in new findings regarding the interplay of interphase, volume fraction and dispersion. Then we present a novel deep learning approach that combines convolutional neural networks with multi-task learning for building quantitative correlations between microstructures and property values. The performance of the model is compared with other state-of-the-art strategies including two-point statistics and structure descriptor-based approaches. Lastly, the interpretation of the deep learning model is investigated to show that the model is able to capture physical understandings while learning. 

The application of Materials Informatics to polymer nanocomposites would result in faster development and commercial implementation of these promising materials, particularly in applications requiring a unique combination of properties. This chapter focuses on a new data resource for nanocomposites — NanoMine — and the tools, models, and algorithms that support data-driven materials design. The chapter begins with a brief introduction to NanoMine, including the data structure and tools available. Critical to the ability to design nanocomposites, however, is developing robust structure–property–processing (s–p–p) relationships. Central to this development is the choice of appropriate microstructure characterization and reconstruction (MCR) techniques that capture a complex morphology and ultimately build statistically equivalent reconstructed composites for accurate modeling of properties. A wide range of MCR techniques is reviewed followed by an introduction of feature selection and feature extraction techniques to identify the most significant microstructure features for dimension reduction. This is then followed by examples of using a descriptor-based representation to create processing–structure (p–s) and structure–property (s–p) relationships for use in design. To overcome the difficulty in modeling the interphase region surrounding nanofillers, an adaptive sampling approach is presented to inversely determine the inter-phase properties based on both FEM simulations and physical experiment data of bulk properties. Finally, a case study for nanodielectrics in a capacitor is introduced to demonstrate the integration of the p–s and s–p relationships to develop optimized materials for achieving multiple desired properties.