Materials Design Problems Research Articles

Active learning for the design of polycrystalline textures using conditional normalizing flows

Generative modeling has opened new avenues for solving previously intractable materials design problems. However, these new opportunities are accompanied by a drastic increase in the required amount of training data. This is in stark juxtaposition to the high expense and difficulty in curating such large materials datasets. In this work, we propose a novel framework for integrating generative models within an active learning loop. This enables the training of generative models with datasets significantly smaller than what has previously been demonstrated, providing a direct route for their application in data constrained environments. The functionality of this framework is then demonstrated by addressing the challenge of designing polycrystalline textures associated with target anisotropic mechanical properties. The developed protocol exhibited a cost reduction between 14 to 18 times over a randomly sampled experimental design.

Generative artificial intelligence and optimisation framework for concrete mixture design with low cost and embodied carbon dioxide

This research presents a generative Artificial Intelligence (AI) and design framework that integrates machine learning (ML) and optimisation methodologies to discover new concrete mixture designs. Unlike traditional ML models that predict based on existing data, this framework innovatively generates new concrete mix designs that meet specific requirements such as strength, cost-efficiency, and reduced embodied CO2. To propose a powerful and reliable generative AI model, several advanced ML algorithms were considered, e.g., CatBoost, XGBoost, and LGBM. These models were trained on a unique dataset consisting of 4,936 data points collected from five different batching plants and have not been published yet. Bayesian Optimisation was employed to fine-tune model hyperparameters, resulting in the most effective models attaining R2 values of 0.94 and 0.89 for raw and grouped data, respectively. To verify the trained generative AI model, a case study was conducted, in which the model was requested to provide designs of a mix with pre-determined strength and optimised cost and embodied CO2. The mix designs generated by the framework were successfully validated through experimental tests, corroborating the predictive outcomes. The research culminated in the development of a web application, a tool crafted to streamline the concrete mixture design and optimisation process. This generative AI design framework can be applied to many other aspects of material design and engineering problems.

Construction and Sampling of Alloy Cluster Expansions—A Tutorial

Crystalline alloys and related mixed systems make up a large family of materials with high tunability that have been proposed as the solution to a large number of energy-related material design problems. Because of the presence of chemical order and disorder in these systems, neither experimental efforts nor computational methods alone are sufficient to span the inherently large configuration space. Therefore, fast and accurate models are necessary. To this end, cluster expansions have been widely and successfully used for the past few decades. Cluster expansions are generalized Ising models designed to predict the energy of any atomic configuration of a system after training on a small subset of the available configurations. Constructing and sampling a cluster expansion consists of multiple steps that have to be performed with care. In this tutorial, we provide a comprehensive guide to this process, highlighting important considerations and potential pitfalls. The tutorial consists of three parts, starting with cluster expansion construction for a relatively simple system, continuing with strategies for more challenging systems such as surfaces, and closing with examples of Monte Carlo sampling of cluster expansions to study order-disorder transitions and phase diagrams. Published by the American Physical Society 2024

Going beyond the Ordered Bulk: A Perspective on the Use of the Cambridge Structural Database for Predictive Materials Design.

When Olga Kennard founded the Cambridge Crystallographic Data Centre in 1965, the Cambridge Structural Database was a pioneering attempt to collect scientific data in a standard format. Since then, it has evolved into an indispensable resource in contemporary molecular materials science, with over 1.25 million structures and comprehensive software tools for searching, visualizing and analyzing the data. In this perspective, we discuss the use of the CSD and CCDC tools to address the multiscale challenge of predictive materials design. We provide an overview of the core capabilities of the CSD and CCDC software and demonstrate their application to a range of materials design problems with recent case studies drawn from topical research areas, focusing in particular on the use of data mining and machine learning techniques. We also identify several challenges that can be addressed with existing capabilities or through new capabilities with varying levels of development effort.

Toward Deep Generation of Guided Wave Representations for Composite Materials

Laminated composite materials are widely used in most fields of engineering. Wave propagation analysis plays an essential role in understanding the short-duration transient response of composite structures. The forward physics-based models are utilized to map from elastic properties space to wave propagation behavior in a laminated composite material. Due to the high-frequency, multi-modal, and dispersive nature of the guided waves, the physics-based simulations are computationally demanding. It makes property prediction, generation, and material design problems more challenging. In this work, a forward physics-based simulator such as the stiffness matrix method is utilized to collect group velocities of guided waves for a set of composite materials. A variational autoencoder (VAE)-based deep generative model is proposed for the generation of new and realistic polar group velocity representations. It is observed that the deep generator is able to reconstruct unseen representations with very low mean square reconstruction error. Global Monte Carlo and directional equally-spaced samplers are used to sample the continuous, complete and organized low-dimensional latent space of VAE. The sampled point is fed into the trained decoder to generate new polar representations. The network has shown exceptional generation capabilities. It is also seen that the latent space forms a conceptual space where different directions and regions show inherent patterns related to the generated representations and their corresponding material properties.

Safeguarding Multi-Fidelity Bayesian Optimization Against Large Model Form Errors and Heterogeneous Noise

Abstract Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas such as materials design. In real-world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the MF data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we view these two limitations and uncertainty sources and address them by building an emulator that more accurately quantifies uncertainties. Specifically, our emulator (1) learns a separate noise model for each data source, and (2) leverages strictly proper scoring rules in regularizing itself. We illustrate the performance of our method through analytical examples and engineering problems in materials design. The comparative studies indicate that our MFBO method outperforms existing technologies, provides interpretable results, and can leverage LF sources which are only locally correlated with the HF source.

Mapping material-property space of cellular metamaterials under uncertainty

Cellular mechanical metamaterials (CMMs) are assemblies of periodic representative volume elements which can be engineered to exhibit unique mechanical properties. Recent advances in additive manufacturing (AM) have enabled us to fabricate sophisticated architected materials with high precision. To increase and diversify applications in both science and engineering practice, the rapid development of fabrication technologies necessities a novel and effective algorithm to outline a theoretical property space for material design problems, allowing designers to acknowledge the limitations of material performance, and to make informed trade-off between target objectives and competing industrial requirements. Inspired by biological evolution, the proposed work addresses a methodology for intuitively mapping material-property spaces of CMMs by using the genetic algorithm as a sampling algorithm, consisting selection of objective properties and stochastic search of property points. It approximates the property space more faithfully and comprehensively than traditional mapping approaches. Considering the manufacturing defects of the AM, uncertainties in properties are quantified via the deep learning method. Variations of properties induced by the defects are illustrated as stochastic boundaries of the property space.

Material stiffness optimization for homogenizing contact stress distribution based on particle swarm optimization using elite opposition-based learning mutation

Rapid advances in computer science and material science have made intelligent algorithms promising for solving material design problems. Particle swarm optimization (PSO) algorithm, as a typical swarm intelligence algorithm, is utilized in this paper as the tool to solve the problem of material stiffness optimization for homogenizing the contact stress distribution. In order to achieve an effective and efficient solution, the opposition-based learning (OBL) technique is introduced and combined with PSO to increases its exploration ability. Two mutation strategies, namely, dimension-by-dimension opposition-based learning and multi-dimensional random opposition-based learning mutation strategies, are further proposed to increase the population diversity of PSO. On this basis, algorithms named DEOBL-PSO and MREOBL-PSO are developed. The developed DEOBL-PSO and MREOBL-PSO are then applied to the field of nonlinear contact in engineering, and the specific problem of material stiffness optimization for homogenizing the contact stress distribution is solved. Impressive results are obtained. The contact stress distributing uniformity is substantially improved by material stiffness optimization using DEOBL-PSO and MREOBL-PSO. Additionally, new relation between material stiffness distribution and contact stress distribution is observed, and the effect of the material stiffness variation range on the contact stress distribution is further explored.

Tailoring the mechanical properties of 3D microstructures: A deep learning and genetic algorithm inverse optimization framework

Materials-by-design has been historically challenging due to complex process-microstructure-property relations. Conventional analytical or simulation-based approaches suffer from low accuracy or long computational time and poor transferability, limiting their applications in solving the inverse material design problem. Here, we establish a deep learning and genetic algorithm framework that integrates forward prediction and inverse exploration. This framework provides an end-to-end solution to achieve application-specific mechanical properties by microstructure optimization. In this study, we select the widely used Ti-6Al-4V alloy to demonstrate the effectiveness and efficiency of this framework. We realize this by tailoring its 3D microstructures to achieve various yield strengths and elastic moduli across a large design space, while minimizing stress concentration factors. Compared with conventional methods, our framework is efficient, versatile, and readily transferrable to a wide range of materials and properties. Paired with emerging additive manufacturing techniques in controlling local microstructural features, our method offers far-reaching potentials for the accelerated development of application-specific, high-performing materials.

A Continuous Action Space Tree search for INverse desiGn (CASTING) framework for materials discovery

Material properties share an intrinsic relationship with their structural attributes, making inverse design approaches crucial for discovering new materials with desired functionalities. Reinforcement Learning (RL) approaches are emerging as powerful inverse design tools, often functioning in discrete action spaces. This constrains their application in materials design problems, which involve continuous search spaces. Here, we introduce an RL-based framework CASTING (Continuous Action Space Tree Search for inverse design), that employs a decision tree-based Monte Carlo Tree Search (MCTS) algorithm with continuous space adaptation through modified policies and sampling. Using representative examples like Silver (Ag) for metals, Carbon (C) for covalent systems, and multicomponent systems such as graphane, boron nitride, and complex correlated oxides, we showcase its accuracy, convergence speed, and scalability in materials discovery and design. Furthermore, with the inverse design of super-hard Carbon phases, we demonstrate CASTING’s utility in discovering metastable phases tailored to user-defined target properties and preferences.

Design of Polymer Nanodielectrics for Capacitive Energy Storage.

Polymer nanodielectrics present a particularly challenging materials design problem for capacitive energy storage applications like polymer film capacitors. High permittivity and breakdown strength are needed to achieve high energy density and loss must be low. Strategies that increase permittivity tend to decrease the breakdown strength and increase loss. We hypothesize that a parameter space exists for fillers of modest aspect ratio functionalized with charge-trapping molecules that results in an increase in permittivity and breakdown strength simultaneously, while limiting increases in loss. In this work, we explore this parameter space, using physics-based, multiscale 3D dielectric property simulations, mixed-variable machine learning and Bayesian optimization to identify the compositions and morphologies which lead to the optimization of these competing properties. We employ first principle-based calculations for interface trap densities which are further used in breakdown strength calculations. For permittivity and loss calculations, we use continuum scale modelling and finite difference solution of Poisson's equation for steady-state currents. We propose a design framework for optimizing multiple properties by tuning design variables including the microstructure and interface properties. Finally, we employ mixed-variable global sensitivity analysis to understand the complex interplay between four continuous microstructural and two categorical interface choices to extract further physical knowledge on the design of nanodielectrics.

The free material design problem for the stationary heat equation on low dimensional structure

For a given balanced distribution of heat sources and sinks, Q, we find an optimal conductivity tensor field, , minimizing the thermal compliance. We present in a rather explicit form in terms of the datum. Our solution is a Borel measure taking values in a cone of non-negative tensors. We present a series of examples with explicit solutions.

Cyclic Solid-Liquid Phase Transformations in the text {CaO}–text {SiO}_2 System—Experiments and Modelling

The cyclic growth and shrinkage of solid oxides (i.e. wollastonite) in text {CaO}–text {SiO}_2-based slags is investigated in-situ by means of High-Temperature Confocal Scanning Laser Microscopy (HT-CSLM). The compositions of the slags are carefully selected to induce different phase transformation conditions, i.e. congruent and incongruent melting/solidification. To complement the experimental results, the kinetics of growth and shrinkage of oxide crystals is investigated by means of a sharp interface model where the interfacial reaction and diffusion in the liquid bulk are considered as possible rate-controlling processes. The modelling approach combined with data analysis from key experiments reveals the underlying dissipative processes of solidification and melting phenomena, here, diffusion in the liquid bulk material and/or the interfacial reactions. The modelling approach is likely to be applicable for future materials design and processing problems from this perspective.

Bayesian optimization with active learning of design constraints using an entropy-based approach

The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints. Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures, as well as possess low density, high thermal conductivity, narrow solidification range, high solidus temperature, and a small linear thermal expansion coefficient. Traditional Integrated Computational Materials Engineering (ICME) methods are not sufficient for exploring combinatorially-vast alloy design spaces, optimizing for multiple objectives, nor ensuring that multiple constraints are met. In this work, we propose an approach for solving a constrained multi-objective materials design problem over a large composition space, specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy (MPEA) for potential use in next-generation gas turbine blades. Our approach is able to learn and adapt to unknown constraints in the design space, making decisions about the best course of action at each stage of the process. As a result, we identify 21 Pareto-optimal alloys that satisfy all constraints. Our proposed framework is significantly more efficient and faster than a brute force approach.

Artificial Intelligence Approaches for Energetic Materials by Design: State of the Art, Challenges, and Future Directions

AbstractArtificial intelligence (AI) is rapidly emerging as a enabling tool for solving complex materials design problems. This paper aims to review recent advances in AI‐driven materials‐by‐design and their applications to energetic materials (EM). Trained with data from numerical simulations and/or physical experiments, AI models can assimilate trends and patterns within the design parameter space, identify optimal material designs (micro‐morphologies, combinations of materials in composites, etc.), and point to designs with superior/targeted property and performance metrics. We review approaches focusing on such capabilities with respect to the three main stages of materials‐by‐design, namely representation learning of microstructure morphology (i. e., shape descriptors), structure‐property‐performance (S−P−P) linkage estimation, and optimization/design exploration. We leave out “process” as much work remains to be done to establish the connectivity between process and structure. We provide a perspective view of these methods in terms of their potential, practicality, and efficacy towards the realization of materials‐by‐design. Specifically, methods in the literature are evaluated in terms of their capacity to learn from a small/limited number of data, computational complexity, generalizability/scalability to other material species and operating conditions, interpretability of the model predictions, and the burden of supervision/data annotation. Finally, we suggest a few promising future research directions for EM materials‐by‐design, such as meta‐learning, active learning, Bayesian learning, and semi‐/weakly‐supervised learning, to bridge the gap between machine learning research and EM research.

Machine learning-based inverse design methods considering data characteristics and design space size in materials design and manufacturing: a review.

In the last few decades, the influence of machine learning has permeated many areas of science and technology, including the field of materials science. This toolkit of data driven methods accelerated the discovery and production of new materials by accurately predicting the complicated physical processes and mechanisms that are not fully described by existing materials theories. However, the availability of a growing number of increasingly complex machine learning models confronts us with the question of "which machine learning algorithm to employ". In this review, we provide a comprehensive review of common machine learning algorithms used for materials design, as well as a guideline for selecting the most appropriate model considering the nature of the design problem. To this end, we classify the material design problems into four categories of: (i) the training data set being sufficiently large to capture the trend of design space (interpolation problem), (ii) a vast design space that cannot be explored thoroughly with the initial training data set alone (extrapolation problem), (iii) multi-fidelity datasets (small accurate dataset and large approximate dataset), and (iv) only a small dataset available. The most successful machine learning-based surrogate models and design approaches will be discussed for each case along with pertinent literature. This review focuses mostly on the use of ML algorithms for the inverse design of complicated composite structures, a topic that has received a lot of attention recently with the rise of additive manufacturing.

Bayesian optimisation for efficient material discovery: a mini review.

Bayesian optimisation (BO) has been increasingly utilised to guide material discovery. While BO is advantageous due to its sample efficiency, flexibility and versatility, it is constrained by a range of core issues including high-dimensional optimisation, mixed search space, multi-objective optimisation and multi-fidelity data. Although various studies have attempted to tackle one or some challenges, a comprehensive BO framework for material discovery is yet to be uncovered. This work provides a short review aiming at connecting algorithmic advancement to material applications. Open algorithmic challenges are discussed and supported by recent material applications. Various open-source packages are compared to assist the selection. Furthermore, three exemplary material design problems are analysed to demonstrate how BO could be useful. The review concludes with an outlook on BO-aided autonomous laboratory.

A multi-fidelity machine learning approach to high throughput materials screening

The ever-increasing capability of computational methods has resulted in their general acceptance as a key part of the materials design process. Traditionally this has been achieved using a so-called computational funnel, where increasingly accurate - and expensive – methodologies are used to winnow down a large initial library to a size which can be tackled by experiment. In this paper we present an alternative approach, using a multi-output Gaussian process to fuse the information gained from both experimental and computational methods into a single, dynamically evolving design. Common challenges with computational funnels, such as mis-ordering methods, and the inclusion of non-informative steps are avoided by learning the relationships between methods on the fly. We show this approach reduces overall optimisation cost on average by around a factor of three compared to other commonly used approaches, through evaluation on three challenging materials design problems.

Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: Extension to geometrical parameterizations

Two-scale simulations are often employed to analyze the effect of the microstructure on a component’s macroscopic properties. Understanding these structure–property relations is essential in the optimal design of materials for specific applications. However, these two-scale simulations are typically computationally expensive and infeasible in multi-query contexts such as optimization and material design. To make such analyses amenable, the microscopic simulations can be replaced by inexpensive-to-evaluate surrogate models. Such surrogate models must be able to handle microstructure parameters in order to be used for material design. A previous work focused on the construction of an accurate surrogate model for microstructures under varying loading and material parameters by combining proper orthogonal decomposition and Gaussian process regression. However, that method works only for a fixed geometry, greatly limiting the design space. This work hence focuses on extending the methodology to treat geometrical parameters. To this end, a method that transforms different geometries onto a parent domain is presented, that then permits existing methodologies to be applied. We propose to solve an auxiliary problem based on linear elasticity to obtain the geometrical transformations. The method has a good reducibility and can therefore be quickly solved for many different geometries. Using these transformations, combined with the nonlinear microscopic problem, we derive a fast-to-evaluate surrogate model with the following key features: (1) the predictions of the effective quantities are independent of the auxiliary problem, (2) the predicted stress fields automatically fulfill the microscopic balance laws and are periodic, (3) the method is non-intrusive, (4) the stress field for all geometries can be recovered, and (5) the sensitivities are available and can be readily used for optimization and material design. The proposed methodology is tested on several composite microstructures, where rotations and large variations in the shape of inclusions are considered. Finally, a two-scale example is shown, where the surrogate model achieves a high accuracy and significant speed up, thus demonstrating its potential in two-scale shape optimization and material design problems.

Dislocation dynamics in heterogeneous nanostructured materials

Crystalline materials can be strengthened by introducing dissimilar phases that impede dislocation glide. At the same time, the changes in microstructure and chemistry usually make the materials less ductile. One way to circumvent the strength–ductility dilemma is to take advantage of heterogeneous nanophases which simultaneously serve as dislocation barriers and sources. Owing to their superior mechanical properties, heterogeneous nanostructured materials (HNMs) have attracted a lot of attention worldwide. Nevertheless, it has been difficult to characterize dislocation dynamics in HNMs using classical continuum models, mainly due to the challenges in describing the elastic and plastic heterogeneity among the phases. In this work, we advance a phase-field dislocation dynamics (PFDD) model to treat multi-phase materials, consisting of phases differing in composition, structural order, and size in the same system. We then apply the advanced PFDD model to exploring two important but divergent materials design problems in HNMs: dislocation/obstacle interactions and dislocation/interface interactions. Results show that the interactions between a dislocation and distribution of obstacles varying in structure and composition cannot be understood by simply interpolating from their individual interactions with a dislocation. It is also found that materials containing interfaces with nanoscale thicknesses and compositional gradients have a much higher dislocation bypass stress than those with sharp interfaces, providing an explanation for the simultaneous high strength and toughness of thick interface-containing nanolaminates as observed in recent experiments.