Deep learning model to predict complex stress and strain fields in hierarchical composites

Single-Image-Based Deep Learning for Precise Atomic Defect Identification

Defect engineering is widely used to impart the desired functionalities on materials. Despite the widespread application of atomic-resolution scanning transmission electron microscopy (STEM), traditional methods for defect analysis are highly sensitive to random noise and human bias. While deep learning (DL) presents a viable alternative, it requires extensive amounts of training data with labeled ground truth. Herein, employing cycle generative adversarial networks (CycleGAN) and U-Nets, we propose a method based on a single experimental STEM image to tackle high annotation costs and image noise for defect detection. Not only atomic defects but also oxygen dopants in monolayer MoS2 are visualized. The method can be readily extended to other two-dimensional systems, as the training is based on unit-cell-level images. Therefore, our results outline novel ways to train the model with minimal data sets, offering great opportunities to fully exploit the power of DL in the materials science community.

Deep Learning for Strain Field Customization in Bioreactor with Dielectric Elastomer Actuator Array

In the field of biomechanics, customizing complex strain fields according to specific requirements poses an important challenge for bioreactor technology, primarily due to the intricate coupling and nonlinear actuation of actuator arrays, which complicates the precise control of strain fields. This paper introduces a bioreactor designed with a 9 × 9 array of independently controllable dielectric elastomer actuators (DEAs), addressing this challenge. We employ image regression-based machine learning for both replicating target strain fields through inverse control and rapidly predicting feasible strain fields generated by the bioreactor in response to control inputs via forward control. To generate training data, a finite element analysis (FEA) simulation model was developed. In the FEA, the device was prestretched, followed by the random assignment of voltages to each pixel, yielding 10,000 distinct output strain field images for the training set. For inverse control, a multilayer perceptron (MLP) is utilized to predict control inputs from images, whereas, for forward control, MLP maps control inputs to low-resolution images, which are then upscaled to high-resolution outputs through a super-resolution generative adversarial network (SRGAN). Demonstrations include inputting biomechanically significant strain fields, where the method successfully replicated the intended fields. Additionally, by using various tumor-stroma interfaces as inputs, the bioreactor demonstrated its ability to customize strain fields accordingly, showcasing its potential as an advanced testbed for tumor biomechanics research.

Elastic parameter identification of three-dimensional soft tissue based on deep neural network

In the field of virtual surgery and deformation simulation, the identification of elastic parameters of human soft tissues is a critical technology that directly affects the accuracy of deformation simulation. Current research on soft tissue deformation simulation predominantly assumes that the elasticity of tissues is fixed and already known, leading to the difficulty in populating with the elasticity measured or identified from specific tissues of real patients. Existing elasticity modeling efforts struggle to be implemented on irregularly structured soft tissues, failing to adapt to clinical surgical practices. Therefore, this paper proposes a new method for identifying human soft tissue elastic parameters based on the finite element method and the deep neural network, UNet. This method requires only the full-field displacement data of soft tissues under external loads to predict their elastic distribution. The performance and validity of the algorithm are assessed using test data and clinical data from rhinoplasty surgeries. Experiments demonstrate that the method proposed in this paper can achieve an accuracy of over 99% in predicting elastic parameters. Clinical data validation shows that the predicted elastic distribution can reduce the error in finite element deformation simulations by more than 80% at the maximum compared to the error with traditional uniform elastic parameters, effectively enhancing the computational accuracy in virtual surgery simulations and soft tissue deformation modeling.

Deep generative spatiotemporal learning for integrating fracture mechanics in composite materials: inverse design, discovery, and optimization

The trade-off between strength and toughness presents a fundamental challenge in engineering material design. Composite materials (CMs) can strategically arrange different materials to enhance both strength and toughness by optimizing the distribution of loads and increasing resistance to crack propagation. However, current data-driven computational modeling approaches for CM configuration optimization suffer from limitations of "substantial computational cost" and "poor predictive power over extrapolation spaces", making it difficult to integrate with global optimization algorithms, and ultimately limiting the discovery of materials with optimal tradeoffs. As a breakthrough, we propose a data-driven design framework with a multi-task DL architecture capable of accurately predicting local fields' spatiotemporal behavior, including stress evolution and crack propagation, alongside homogenized mechanical properties. Our model, trained on datasets generated from crack phase fields simulations of random configurations, demonstrated exceptional predictive performance even for unseen configurations with well organized patterns exploiting nature-inspired morphological features. Importantly, solely from composite material (CM) configurations, our model effectively predicts long-term spatiotemporal fields with an accuracy comparable to FEM but with a substantial reduction in computational time. By coupling the model's predictive power with genetic optimization algorithms, we demonstrated the framework's applicability in two representative inverse design tasks: devising CM configurations with mechanical properties beyond the training set and guiding desired crack pattern formation. Our research highlights the potential of artificial intelligence as a feasible alternative to conventional computational approaches for straightforward configurational and structural optimization.

Mechanical Field Guiding Structure Design Strategy for Meta-Fiber Reinforced Hydrogel Composites by Deep Learning

Fiber-reinforced hydrogel composites are widely employed in many engineering applications, such as drug release, and flexible electronics, with more flexible mechanical properties than pure hydrogel materials. Comparing to the hydrogel strengthened by continuous fiber, the meta-fiber reinforced hydrogel provides stronger individualized design ability of deformation patterns and tunable stiffness, especially for the elaborate applications in joint, cartilage, and organ. In this paper, a novel structure design strategy based on deep learning algorithm is proposed for hydrogel reinforced by meta-fiber to achieve targeted mechanical properties, such as stress and displacement fields. A solid mechanic model for meta-fiber reinforced hydrogel is first developed to construct the dataset of fiber distribution and the corresponding mechanical properties of the composite. Generative adversarial network (GAN) is then trained to characterize the relationship between stress or displacement field, and meta-fiber distribution. The well-trained GAN is implemented to design meta-fiber reinforced hydrogel composite structure under specific operation conditions. The results show that the deep learning method may efficiently predict the structure of the hydrogel composite with satisfied confidence, and has great potential for applications in drug delivery and flexible electronics.

ForceGen: End-to-end de novo protein generation based on nonlinear mechanical unfolding responses using a language diffusion model

Through evolution, nature has presented a set of remarkable protein materials, including elastins, silks, keratins and collagens with superior mechanical performances that play crucial roles in mechanobiology. However, going beyond natural designs to discover proteins that meet specified mechanical properties remains challenging. Here, we report a generative model that predicts protein designs to meet complex nonlinear mechanical property-design objectives. Our model leverages deep knowledge on protein sequences from a pretrained protein language model and maps mechanical unfolding responses to create proteins. Via full-atom molecular simulations for direct validation, we demonstrate that the designed proteins are de novo, and fulfill the targeted mechanical properties, including unfolding energy and mechanical strength, as well as the detailed unfolding force-separation curves. Our model offers rapid pathways to explore the enormous mechanobiological protein sequence space unconstrained by biological synthesis, using mechanical features as the target to enable the discovery of protein materials with superior mechanical properties.

Unbiased construction of constitutive relations for soft materials from experiments via rheology-informed neural networks

The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material.

Rapid and accurate predictions of perfect and defective material properties in atomistic simulation using the power of 3D CNN-based trained artificial neural networks

This article introduces an innovative approach that utilizes machine learning (ML) to address the computational challenges of accurate atomistic simulations in materials science. Focusing on the field of molecular dynamics (MD), which offers insight into material behavior at the atomic level, the study demonstrates the potential of trained artificial neural networks (tANNs) as surrogate models. These tANNs capture complex patterns from built datasets, enabling fast and accurate predictions of material properties. The article highlights the application of 3D convolutional neural networks (CNNs) to incorporate atomistic details and defects in predictions, a significant advancement compared to current 2D image-based, or descriptor-based methods. Through a dataset of atomistic structures and MD simulations, the trained 3D CNN achieves impressive accuracy, predicting material properties with a root-mean-square error below 0.65 GPa for the prediction of elastic constants and a speed-up of approximately 185 to 2100 times compared to traditional MD simulations. This breakthrough promises to expedite materials design processes and facilitate scale-bridging in materials science, offering a new perspective on addressing computational demands in atomistic simulations.

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.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

Mechanical metamaterials are meticulously designed structures with exceptional mechanical properties determined by their microstructures and constituent materials. Tailoring their material and geometric distribution unlocks the potential to achieve unprecedented bulk properties and functions. However, current mechanical metamaterial design considerably relies on experienced designers' inspiration through trial and error, while investigating their mechanical properties and responses entails time-consuming mechanical testing or computationally expensive simulations. Nevertheless, recent advancements in deep learning have revolutionized the design process of mechanical metamaterials, enabling property prediction and geometry generation without prior knowledge. Furthermore, deep generative models can transform conventional forward design into inverse design. Many recent studies on the implementation of deep learning in mechanical metamaterials are highly specialized, and their pros and cons may not be immediately evident. This critical review provides a comprehensive overview of the capabilities of deep learning in property prediction, geometry generation, and inverse design of mechanical metamaterials. Additionally, this review highlights the potential of leveraging deep learning to create universally applicable datasets, intelligently designed metamaterials, and material intelligence. This article is expected to be valuable not only to researchers working on mechanical metamaterials but also those in the field of materials informatics.

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.

Physics-supervised deep learning-based optimization (PSDLO) with accuracy and efficiency

Identifying efficient and accurate optimization algorithms is a long-desired goal for the scientific community. At present, a combination of evolutionary and deep-learning methods is widely used for optimization. In this paper, we demonstrate three cases involving different physics and conclude that no matter how accurate a deep-learning model is for a single, specific problem, a simple combination of evolutionary and deep-learning methods cannot achieve the desired optimization because of the intrinsic nature of the evolutionary method. We begin by using a physics-supervised deep-learning optimization algorithm (PSDLO) to supervise the results from the deep-learning model. We then intervene in the evolutionary process to eventually achieve simultaneous accuracy and efficiency. PSDLO is successfully demonstrated using both sufficient and insufficient datasets. PSDLO offers a perspective for solving optimization problems and can tackle complex science and engineering problems having many features. This approach to optimization algorithms holds tremendous potential for application in real-world engineering domains.

A Comprehensive and Versatile Multimodal Deep-Learning Approach for Predicting Diverse Properties of Advanced Materials

A multimodal deep-learning (MDL) framework is presented for predicting physical properties of a ten-dimensional acrylic polymer composite material by merging physical attributes and chemical data. The MDL model comprises four modules, including three generative deep-learning models for material structure characterization and a fourth model for property prediction. The approach handles an 18-dimensional complexity, with ten compositional inputs and eight property outputs, successfully predicting 913 680 property data points across 114 210 composition conditions. This level of complexity is unprecedented in computational materials science, particularly for materials with undefined structures. A framework is proposed to analyze the high-dimensional information space for inverse material design, demonstrating flexibility and adaptability to various materials and scales, provided sufficient data are available. This study advances future research on different materials and the development of more sophisticated models, drawing the authors closer to the ultimate goal of predicting all properties of all materials.

Fill in the Blank: Transferrable Deep Learning Approaches to Recover Missing Physical Field Information

Solving materials engineering tasks is often hindered by limited information, such as in inverse problems with only boundary data information or design tasks with a simple objective but a vast search space. To address these challenges, multiple deep learning (DL) architectures are leveraged to predict missing mechanical information given limited known data in part of the domain, and further characterize the composite geometries from the recovered mechanical fields for 2D and 3D complex microstructures. In 2D, a conditional generative adversarial network (GAN) is utilized to complete partially masked field maps and predict the composite geometry with convolutional models with great accuracy and generality by making precise predictions on field data with mixed stress/strain components, hierarchical geometries, distinct materials properties and various types of microstructures including ill-posed inverse problems. In 3D, a Transformer-based architecture is implemented to predict complete 3D mechanical fields from input field snapshots. The model manifests excellent performance regardless of microstructural complexity and recovers the entire bulk field even from a single surface field image, allowing internal structural characterization from only boundary measurements. The whole frameworks provide efficient ways for analysis and design with incomplete information and allow the direct inverse translation from properties back to materials structures.

An interpretable deep learning approach for designing nanoporous silicon nitride membranes with tunable mechanical properties

The high permeability and strong selectivity of nanoporous silicon nitride (NPN) membranes make them attractive in a broad range of applications. Despite their growing use, the strength of NPN membranes needs to be improved for further extending their biomedical applications. In this work, we implement a deep learning framework to design NPN membranes with improved or prescribed strength values. We examine the predictions of our framework using physics-based simulations. Our results confirm that the proposed framework is not only able to predict the strength of NPN membranes with a wide range of microstructures, but also can design NPN membranes with prescribed or improved strength. Our simulations further demonstrate that the microstructural heterogeneity that our framework suggests for the optimized design, lowers the stress concentration around the pores and leads to the strength improvement of NPN membranes as compared to conventional membranes with homogenous microstructures.

Programming 3D curved mesosurfaces using microlattice designs

Cellular microstructures form naturally in many living organisms (e.g., flowers and leaves) to provide vital functions in synthesis, transport of nutrients, and regulation of growth. Although heterogeneous cellular microstructures are believed to play pivotal roles in their three-dimensional (3D) shape formation, programming 3D curved mesosurfaces with cellular designs remains elusive in man-made systems. We report a rational microlattice design that allows transformation of 2D films into programmable 3D curved mesosurfaces through mechanically guided assembly. Analytical modeling and a machine learning-based computational approach serve as the basis for shape programming and determine the heterogeneous 2D microlattice patterns required for target 3D curved surfaces. About 30 geometries are presented, including both regular and biological mesosurfaces. Demonstrations include a conformable cardiac electronic device, a stingray-like dual mode actuator, and a 3D electronic cell scaffold.

Detecting Microstructural Criticality/Degeneracy through Hybrid Learning Strategies Trained by Molecular Dynamics Simulations

Efficient microstructure design can strongly accelerate the development of materials. However, the complexity of the microstructure-behavior relation renders the criticalities and degeneracies within the microstructure space highly possible. Criticality means that a slight microstructural change can lead to a dramatic transition in material behavior, while degeneracy means that very different microstructures may lead to similar behaviors. To investigate these microstructural characteristics of the fiber/matrix interface within composite materials, we have proposed a hybrid deep-learning-based framework by integrating the supervised feed-forward neural network and the unsupervised autoencoder, which are trained by the molecular dynamics (MD) simulation results. The well-trained model continuously maps the elemental density images within the interfacial area into a low-dimensional latent space. Assisted by the extracted latent features, we can easily detect the criticalities and degeneracies within the original microstructure space of the composite's interface. The predicted microstructural criticalities and degeneracies are validated by investigating their atomistic origins through MD simulations. The proposed framework can be employed for the interfacial microstructure design of composite materials by identifying certain interfacial microstructures that might lead to undesirable behaviors.

Designing Bioinspired Composite Structures via Genetic Algorithm and Conditional Variational Autoencoder

Designing composite materials with tailored stiffness and toughness is challenging due to the massive number of possible material and geometry combinations. Although various studies have applied machine learning techniques and optimization methods to tackle this problem, we still lack a complete understanding of the material effects at different positions and a systematic experimental procedure to validate the results. Here we study a two-dimensional (2D) binary composite system with an edge crack and grid-like structure using a Genetic Algorithm (GA) and Conditional Variational Autoencoder (CVAE), which can design a composite with desired stiffness and toughness. The fitness of each design is evaluated using the negative mean square error of their predicted stiffness and toughness and the target values. We use finite element simulations to generate a machine-learning dataset and perform tensile tests on 3D-printed specimens to validate our results. We show that adding soft material behind the crack tip, instead of ahead of the tip, tremendously increases the overall toughness of the composite. We also show that while GA generates composite designs with slightly better accuracy (both methods perform well, with errors below 20%), CVAE takes considerably less time (~1/7500) to generate designs. Our findings may provide insights into the effect of adding soft material at different locations of a composite system and may also provide guidelines for conducting experiments and Explainable Artificial Intelligence (XAI) to validate the results.

Predicting stress, strain and deformation fields in materials and structures with graph neural networks

Developing accurate yet fast computational tools to simulate complex physical phenomena is a long-standing problem. Recent advances in machine learning have revolutionized the way simulations are approached, shifting from a purely physics- to AI-based paradigm. Although impressive achievements have been reached, efficiently predicting complex physical phenomena in materials and structures remains a challenge. Here, we present an AI-based general framework, implemented through graph neural networks, able to learn complex mechanical behavior of materials from a few hundreds data. Harnessing the natural mesh-to-graph mapping, our deep learning model predicts deformation, stress, and strain fields in various material systems, like fiber and stratified composites, and lattice metamaterials. The model can capture complex nonlinear phenomena, from plasticity to buckling instability, seemingly learning physical relationships between the predicted physical fields. Owing to its flexibility, this graph-based framework aims at connecting materials' microstructure, base materials' properties, and boundary conditions to a physical response, opening new avenues towards graph-AI-based surrogate modeling.

Multiscale Modeling at the Interface of Molecular Mechanics and Natural Language through Attention Neural Networks

Humans are continually bombarded with massive amounts of data. To deal with this influx of information, we use the concept of attention in order to perceive the most relevant input from vision, hearing, touch, and others. Thereby, the complex ensemble of signals is used to generate output by querying the processed data in appropriate ways. Attention is also the hallmark of the development of scientific theories, where we elucidate which parts of a problem are critical, often expressed through differential equations. In this Account we review the emergence of attention-based neural networks as a class of approaches that offer many opportunities to describe materials across scales and modalities, including how universal building blocks interact to yield a set of material properties. In fact, the self-assembly of hierarchical, structurally complex, and multifunctional biomaterials remains a grand challenge in modeling, theory, and experiment. Expanding from the process by which material building blocks physically interact to form a type of material, in this Account we view self-assembly as both the functional emergence of properties from interacting building blocks as well as the physical process by which elementary building blocks interact and yield structure and, thereby, functions. This perspective, integrated through the theory of materiomics, allows us to solve multiscale problems with a first-principles-based computational approach based on attention-based neural networks that transform information to feature to property while providing a flexible modeling approach that can integrate theory, simulation, and experiment. Since these models are based on a natural language framework, they offer various benefits including incorporation of general domain knowledge via general-purpose pretraining, which can be accomplished without labeled data or large amounts of lower-quality data. Pretrained models then offer a general-purpose platform that can be fine-tuned to adapt these models to make specific predictions, often with relatively little labeled data. The transferrable power of the language-based modeling approach realizes a neural olog description, where mathematical categorization is learned by multiheaded attention, without domain knowledge in its formulation. It can hence be applied to a range of complex modeling tasks─such as physical field predictions, molecular properties, or structure predictions, all using an identical formulation. This offers a complementary modeling approach that is already finding numerous applications, with great potential to solve complex assembly problems, enabling us to learn, build, and utilize functional categorization of how building blocks yield a range of material functions. In this Account, we demonstrate the approach in various application areas, including protein secondary structure prediction and prediction of normal-mode frequencies as well as predicting mechanical fields near cracks. Unifying these diverse problem areas is the building block approach, where the models are based on a universally applicable platform that offers benefits ranging from transferability, interpretability, and cross-domain pollination of knowledge as exemplified through a transformer model applied to predict how musical compositions infer de novo protein structures. We discuss future potentialities of this approach for a variety of material phenomena across scales, including the use in multiparadigm modeling schemes.

Modeling Atomistic Dynamic Fracture Mechanisms Using a Progressive Transformer Diffusion Model

Dynamic fracture is an important area of materials analysis, assessing the atomic-level mechanisms by which materials fail over time. Here, we focus on brittle materials failure and show that an atomistically derived progressive transformer diffusion machine learning model can effectively describe the dynamics of fracture, capturing important aspects such as crack dynamics, instabilities, and initiation mechanisms. Trained on a small dataset of atomistic simulations, the model generalizes well and offers a rapid assessment of dynamic fracture mechanisms for complex geometries, expanding well beyond the original set of atomistic simulation results. Various validation cases, progressively more distinct from the data used for training, are presented and analyzed. The validation cases feature distinct geometric details, including microstructures generated by a generative neural network used here to identify novel bio-inspired material designs for mechanical performance. For all cases, the model performs well and captures key aspects of material failure.

Learning the stress-strain fields in digital composites using Fourier neural operator

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely challenging due to the innumerable design combinations and prohibitive computational costs for physics-based solvers. In this study, we employ a neural operator-based framework, namely Fourier neural operator (FNO), to learn the mechanical response of 2D composites. We show that the FNO exhibits high-fidelity predictions of the complete stress and strain tensor fields for geometrically complex composite microstructures with very few training data and purely based on the microstructure. The model also exhibits zero-shot generalization on unseen arbitrary geometries with high accuracy. Furthermore, the model exhibits zero-shot super-resolution capabilities by predicting high-resolution stress and strain fields directly from low-resolution input configurations. Finally, the model also provides high-accuracy predictions of equivalent measures for stress-strain fields, allowing realistic upscaling of the results.

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Predict stress and strain tensors directly from the microstructure

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Demonstrate material and pixel-wise super-resolution of the FNO model

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Zero-shot generalization to unseen arbitrary geometries

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Measuring equivalent quantities such as von-mises stress and equivalent strains

Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy

Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy-absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress-strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy-absorbing systems, soft robots, and morphing structures.

High-Throughput Generation of 3D Graphene Metamaterials and Property Quantification Using Machine Learning

3D graphene assemblies are proposed as solutions to meet the goal toward efficient utilization of 2D graphene sheets, showing excellent performances in applications such as mechanical support, energy storage, and electrochemical catalysis. However, given the diversity and complexity of possible graphene 3D structures, there does not yet exist a systematic approach that can generate target 3D shapes and also, evaluate their performance. Here high-throughput data generation is combined with artificial intelligence approaches to realize rapid structure formation and property quantification of 3D graphene foams with mathematically controlled topologies, driven by molecular dynamics simulations. More than 4000 different foam structures are created, which feature diverse topologies that contain potential pathways for small molecules and auxetic structures with negative Poisson's ratio. Empowered by machine learning (ML) algorithms including graph neural networks, not only global properties such as elastic moduli, but also local behaviors such as atomic stress can be predicted and optimized based on their atomic structure, bypassing expensive atomistic simulations. The key findings of the research reported in this paper include a high-throughput virtual framework of generating diverse 3D graphene assemblies with mechanical performances quantification, and highly efficient methods of evaluating physical properties based on ML.

Prediction of atomic stress fields using cycle-consistent adversarial neural networks based on unpaired and unmatched sparse datasets

Deep learning holds great promise for applications in materials science, including the discovery of physical laws and materials design. However, the availability of proper data remains a challenge - often, data lacks labels, or does not contain direct pairing between input and output property of interest. Here we report an approach based on an adversarial neural network model - composed of four individual deep neural nets - to yield atomistic-level prediction of stress fields directly from an input atomic microstructure, illustrated here for defected graphene sheets under tension. The primary question we address is whether it is possible to predict stress fields without any microstructure-to-stress fields pairings, nor the existence of any input-output pairs whatsoever, in the dataset. Using a cycle-consistent adversarial neural net with either U-Net, ResNet and a hybrid U-Net-ResNet architecture, applied to a system of graphene lattices with defects we devise an algorithmic framework that enables us to successfully train and validate a model that reliably predicts atomistic-level field data of unknown microstructures, generalizing to reproduce well-known nano- and micromechanical features such as stress concentrations, size effects, and crack shielding. In a series of validation analyses, we show that the model closely reproduces reactive molecular dynamics simulations but at significant computational efficiency, and without a priori knowledge of any physical laws that govern this complex fracture problem. The model opens an avenue for upscaling where the mechanistic insights, and predictions from the model, can be used to construct analyses of very large systems, based off relatively small and sparse datasets. Since the model is trained to achieve cycle consistency, a trained model features both forward (microstructure to stress) and inverse (stress to microstructure) generators; offering potential applications in materials design to achieve a certain stress field. Another application is the prediction of stress fields based off experimentally acquired structural data, where the knowledge of solely positions of atoms is sufficient to predict physical quantities for augmentation or analysis processes.

Studying Complex Evolution of Hyperelastic Materials under External Field Stimuli using Artificial Neural Networks with Spatiotemporal Features in a Small-Scale Dataset

Deep-learning (DL) methods, in consideration of their excellence in dealing with highly complex structure-performance relationships for materials, are expected to become a new design paradigm for breakthroughs in material performance. However, in most cases, it is impractical to collect massive-scale experimental data or open-source theoretical databases to support training DL models with sufficient prediction accuracy. In a dataset consisting of 483 porous silicone rubber observations generated via ink-writing additive manufacturing, this work demonstrates that constructing low-dimensional, accurate descriptors is the prerequisite for obtaining high-precision DL models based on small experimental datasets. On this basis, a unique convolutional bidirectional long short-term memory model with spatiotemporal features extraction capability is designed, whose hierarchical learning mechanism further reduces the requirement for the amount of data by taking full advantage of data information. The proposed approach can be expected as a powerful tool for innovative material design on small experimental datasets, which can also be used to explore the evolutionary mechanisms of the structures and properties of materials under complex working conditions.

Design, manufacture, and testing of customized sterilizable respirator

The respirator as one of the personal protective equipment is essential for industrial activities (e.g., mining, painting, woodcutting, manufacturing) for protection from contaminants in the air and during the Covid-19 pandemic to protect the wearer from infection. The respirators nowadays are commonly made of rigid plastic. They are expensive, cumbersome, and not comfortable to wear. The many components with complex structures prevent it from cleaning and reusing. We develop a practical and scalable strategy to create customized respirators with durability using computational modeling and 3D printing. It is shown that by morphing the shape according to the user's photo, the respirator is designed to fit a user's face without air leaks. Using a printing-mold-casting method, this respirator can be manufactured by silicone rubber with accuracy, which is highly durable, with its mechanics primarily not affected by sterilization. These features provide the current respirator adaptivity and convenience in carrying and storing, as well as more comfort for long-time wearing.

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.

Rapid prediction of protein natural frequencies using graph neural networks

Natural vibrational frequencies of proteins help to correlate functional shifts with sequence or geometric variations that lead to negligible changes in protein structures, such as point mutations related to disease lethality or medication effectiveness. Normal mode analysis is a well-known approach to accurately obtain protein natural frequencies. However, it is not feasible when high-resolution protein structures are not available or time consuming to obtain. Here we provide a machine learning model to directly predict protein frequencies from primary amino acid sequences and low-resolution structural features such as contact or distance maps. We utilize a graph neural network called principal neighborhood aggregation, trained with the structural graphs and normal mode frequencies of more than 34 000 proteins from the protein data bank. combining with existing contact/distance map prediction tools, this approach enables an end-to-end prediction of the frequency spectrum of a protein given its primary sequence.

We present a computational framework based on graph neural networks (GNNs) to predict the natural frequencies of proteins from primary amino acid sequences and contact/distance maps.

Transferable, Deep-Learning-Driven Fast Prediction and Design of Thermal Transport in Mechanically Stretched Graphene Flakes

Piling graphene sheets into a bulk form is essential for achieving massive applications of graphene in flexible structures and devices, and the arbitrary shape, random distributions, and adjacent overlaps of graphene sheets are yet challenging the prediction of its fundamental properties that are strongly coupled by mechanical strength and thermal or electronic transport. Here, we present a deep neural network (DNN)-based machine learning (ML) approach that enables the prediction of thermal conductivity of piled graphene structures with a broad range of geometric configurations and dimensions in response to external mechanical loading. A physics-informed pixel value matrix is developed to capture the key geometric features of piled graphene structures and is incorporated into the DNN to train the ML model with the only training data ratio of 12.5% but the prediction accuracy of 94%. The ML model is further extended with the transferred knowledge from primitive training data sets to predict the thermal transport of piled graphene in a custom data set. Extensive demonstrations in search of piled graphene structures with desirable thermal conductivity and its response to mechanical loading are presented and illustrate the capability and accuracy of the DNN-ML model for establishing a mechanically adaptive structure: responsive thermal property paradigm in piled graphene. This work lays a foundation for quantitatively evaluating thermal conductivity of piled graphene in response to mechanical loadings through an ML model and also offers a rational route for exploring mechanically tunable thermal properties of nanomaterial-based bulk forms, potentially useful in the design of flexible thermal structures and devices with controllable thermal management performance.

Analysis on Microstructure-Property Linkages of Filled Rubber Using Machine Learning and Molecular Dynamics Simulations

A better understanding of the microstructure–property relationship can be achieved by sampling and analyzing a microstructure leading to a desired material property. During the simulation of filled rubber, this approach includes extracting common aggregates from a complex filler morphology consisting of hundreds of filler particles. However, a method for extracting a core structure that determines the rubber mechanical properties has not been established yet. In this study, we analyzed complex filler morphologies that generated extremely high stress using two machine learning techniques. First, filler morphology was quantified by persistent homology and then vectorized using persistence image as the input data. After that, a binary classification model involving logistic regression analysis was developed by training a dataset consisting of the vectorized morphology and stress-based class. The filler aggregates contributing to the desired mechanical properties were extracted based on the trained regression coefficients. Second, a convolutional neural network was employed to establish a classification model by training a dataset containing the imaged filler morphology and class. The aggregates strongly contributing to stress generation were extracted by a kernel. The aggregates extracted by both models were compared, and their shapes and distributions producing high stress levels were discussed. Finally, we confirmed the effects of the extracted aggregates on the mechanical property, namely the validity of the proposed method for extracting stress-contributing fillers, by performing coarse-grained molecular dynamics simulations.