Physically informed artificial neural networks for atomistic modeling of materials

Uncertainty Based Machine Learning-DFT Hybrid Framework for Accelerating Geometry Optimization

Geometry optimization is an important tool used for computational simulations in the fields of chemistry, physics, and material science. Developing more efficient and reliable algorithms to reduce the number of force evaluations would lead to accelerated computational modeling and materials discovery. Here, we present a delta method-based neural network-density functional theory (DFT) hybrid optimizer to improve the computational efficiency of geometry optimization. Compared to previous active learning approaches, our algorithm adds two key features: a modified delta method incorporating force information to enhance efficiency in uncertainty estimation, and a quasi-Newton approach based upon a Hessian matrix calculated from the neural network; the later improving stability of optimization near critical points. We benchmarked our optimizer against commonly used optimization algorithms using systems including bulk metal, metal surface, metal hydride, and an oxide cluster. The results demonstrate that our optimizer effectively reduces the number of DFT force calls by 2-3 times in all test systems.

Improved medical waste plasma gasification modelling based on implicit knowledge-guided interpretable machine learning

Ensuring the interpretability of machine learning models in chemical engineering remains challenging due to inherent limitations and data quality issues, hindering their reliable application. In this study, a qualitatively implicit knowledge-guided machine learning framework is proposed to improve plasma gasification modelling. Starting with a pre-trained machine learning model, parameters are further optimized by integrating the heuristic algorithm to minimize the data fitting errors and resolving implicit monotonic inconsistencies. The latter is comprehensively quantified through Monte Carlo simulations. This framework is adaptive to different machine learning techniques, exemplified by artificial neural network (ANN) and support vector machine (SVM) in this study. Validated by a case study on plasma gasification, the results reveal that the improved models achieve better generalizability and scientific interpretability in predicting syngas quality. Specifically, for ANN, the root mean square error (RMSE) and knowledge-based error (KE) reduce by 36.44% and 83.22%, respectively, while SVM displays a decrease of 2.58% in RMSE and a remarkable 100% in KE. Importantly, the improved models successfully capture all desired implicit monotonicity relationships between syngas quality and feedstock characteristics/operating parameters, addressing a limitation that traditional machine learning struggles with.

A molecular dynamics simulation study of thermal conductivity of plumbene

We investigate the lattice thermal conductivity of plumbene using molecular dynamics simulations, overcoming existing limitations by optimizing the parameters of Tersoff and Stillinger-Weber potentials via artificial neural networks. Our findings indicate that at room temperature, the thermal conductivity of a 1050 Å × 300 Å plumbene sheet is approximately 8 W m-1 K-1, significantly lower (23%) than that of bulk lead. Our analysis elucidates that thermal conductivity is enhanced by increased sample length, while it is reduced by temperature. Moreover, plumbene samples with zigzag edges display superior thermal conductivity compared to those with armchair edges. In addition, the thermal conductivity of plumbene exhibits an increase at low tensile strains, whereas it decreases as the strains become larger. This investigation provides crucial insights into the thermal conductivity behavior of plumbene under varying conditions.

Accurate Crystal Structure Prediction of New 2D Hybrid Organic-Inorganic Perovskites

Low-dimensional hybrid organic-inorganic perovskites (HOIPs) are promising electronically active materials for light absorption and emission. The design space of HOIPs is extremely large, as a variety of organic cations can be combined with different inorganic frameworks. This not only allows for tunable electronic and mechanical properties but also necessitates the development of new tools for in silico high throughput analysis of candidate materials. In this work, we present an accurate, efficient, and widely applicable machine learning interatomic potential (MLIP) trained on 86 diverse experimentally reported HOIP materials. This MLIP was tested on 73 experimentally reported perovskite compositions and achieves a high accuracy, relative to density functional theory (DFT). We also introduce a novel random structure search algorithm designed for the crystal structure prediction of 2D HOIPs. The combination of MLIP and the structure search algorithm reliably recovers the crystal structure of 14 known 2D perovskites by specifying only the organic molecule and inorganic cation/halide. Performing this crystal structure search with ab initio methods would be computationally prohibitive but is relatively inexpensive with the MLIP. Finally, the developed procedure is used to predict the structure of a totally new HOIP with cation (cis-1,3-cyclohexanediamine). Subsequently, the new compound was synthesized and characterized, which matches the predicted structure, confirming the accuracy of our method. This capability will enable the efficient and accurate screening of thousands of combinations of organic cations and inorganic layers for further investigation.

Synergistic Integration of Physical Embedding and Machine Learning Enabling Precise and Reliable Force Field

Machine-learning force fields have achieved significant strides in accurately reproducing the potential energy surface with quantum chemical accuracy. However, this approach still faces several challenges, e.g., extrapolating to uncharted chemical spaces, interpreting long-range electrostatics, and mapping complex macroscopic properties. To address these issues, we advocate for a synergistic integration of physical principles and machine learning techniques within the framework of a physically informed neural network (PINN). This approach involves incorporating physical knowledge into the parameters of the neural network, coupled with an efficient global optimizer, the Tabu-Adam algorithm, proposed in this work to augment optimization under strict physical constraint. We choose the AMOEBA+ force field as the physics-based model for embedding and then train and test it using the diethylene glycol dimethyl ether (DEGDME) data set as a case study. The results reveal a breakthrough in constructing a precise and noise-robust machine learning force field. Utilizing two training sets with hundreds of samples, our model exhibits remarkable generalization and density functional theory (DFT) accuracy in describing molecular interactions and enables a precise prediction of the macroscopic properties such as the diffusion coefficient with minimal cost. This work provides valuable insight into establishing a fundamental framework of the PINN force field.

Improving Molecular-Dynamics Simulations for Solid-Liquid Interfaces with Machine-Learning Interatomic Potentials

Emerging developments in artificial intelligence have opened infinite possibilities for material simulation. Depending on the powerful fitting of machine learning algorithms to first-principles data, machine learning interatomic potentials (MLIPs) can effectively balance the accuracy and efficiency problems in molecular dynamics (MD) simulations, serving as powerful tools in various complex physicochemical systems. Consequently, this brings unprecedented enthusiasm for researchers to apply such novel technology in multiple fields to revisit the major scientific problems that have remained controversial owing to the limitations of previous computational methods. Herein, we introduce the evolution of MLIPs, provide valuable application examples for solid-liquid interfaces, and present current challenges. Driven by solving multitudinous difficulties in terms of the accuracy, efficiency, and versatility of MLIPs, this booming technique, combined with molecular simulation methods, will provide an underlying and valuable understanding of interdisciplinary scientific challenges, including materials, physics, and chemistry.

Active sparse Bayesian committee machine potential for isothermal-isobaric molecular dynamics simulations

Recent advancements in machine learning potentials (MLPs) have significantly impacted the fields of chemistry, physics, and biology by enabling large-scale first-principles simulations. Among different machine learning approaches, kernel-based MLPs distinguish themselves through their ability to handle small datasets, quantify uncertainties, and minimize over-fitting. Nevertheless, their extensive computational requirements present considerable challenges. To alleviate these, sparsification methods have been developed, aiming to reduce computational scaling without compromising accuracy. In the context of isothermal and isobaric ML molecular dynamics (MD) simulations, achieving precise pressure estimation is crucial for reproducing reliable system behavior under constant pressure. Despite progress, sparse kernel MLPs struggle with precise pressure prediction. Here, we introduce a virial kernel function that significantly enhances the pressure estimation accuracy of MLPs. Additionally, we propose the active sparse Bayesian committee machine (BCM) potential, an on-the-fly MLP architecture that aggregates local sparse Gaussian process regression (SGPR) MLPs. The sparse BCM potential overcomes the steep computational scaling with the kernel size, and a predefined restriction on the size of kernel allows for fast and efficient on-the-fly training. Our advancements facilitate accurate and computationally efficient machine learning-enhanced MD (MLMD) simulations across diverse systems, including ice-liquid coexisting phases, Li10Ge(PS6)2 lithium solid electrolyte, and high-pressure liquid boron nitride.

Theoretical calculations and simulations power the design of inorganic solid-state electrolytes

Using solid-state electrolytes (SSEs) to build batteries helps improve the safety and lifespan of batteries, making it crucial to deeply understand the fundamental physical and chemical properties of SSEs. Theoretical calculations based on modern quantum chemical methods and molecular simulation techniques can explore the relationship between the structure and performance of SSEs at the atomic and molecular levels. In this review, we first comprehensively introduce theoretical methods used to assess the stability of SSEs, including mechanical, phase, and electrochemical stability, and summarize the significant progress achieved through these methods. Next, we outline the methods for calculating ion diffusion properties and discuss the advantages and limitations of these methods by combining the diffusion behaviors and mechanisms of ions in the bulk phase, grain boundaries, and electrode-solid electrolyte interfaces. Finally, we summarize the latest research progress in the discovery of high-quality SSEs through high-throughput screening and machine learning and discuss the application prospects of a new mode that incorporates machine learning into high-throughput screening.

Reaction Templates: Bridging Synthesis Knowledge and Artificial Intelligence

ConspectusThe field of chemical research boasts a long history of developing software to automate synthesis planning and reaction prediction. Early software relied heavily on expert systems, requiring significant effort to encode vast amounts of synthesis knowledge into a computer-readable format. However, recent advancements in deep learning have shifted the focus toward AI models, offering improved prediction capabilities. Despite these advancements, current AI models often lack the integration of known synthesis rules and intuitions, creating a gap that hinders interpretability and future development of the models. To bridge them, our research group has been actively working on incorporating reaction templates into deep learning models, achieving promising results across various applications.In this Account, we present our latest works to incorporate the known synthesis knowledge into the deep learning models through the utilization of reaction templates. We begin by highlighting the limitations of early computer programs heavily reliant on hand-coded rules. These programs, while providing a foundation for the field, presented limitations in scalability and adaptability. We then introduce SMARTS (SMILES arbitrary target specification), a popular Python-readable format for representing chemical reactions. This format of reaction encoding facilitates the quick integration of synthesis knowledge into AI models built using the Python language. With the SMARTS-based reaction templates, we introduce our recent efforts of developing an AI model for reaction-based molecule optimization. Subsequently, we discuss the recent efforts to automate the extraction of reaction templates from vast chemical reaction databases. This approach eliminates the previously required manual effort of encoding knowledge, a process that could be time-consuming and prone to error when dealing with large data sets. By customizing the automated extraction algorithm, we have developed powerful AI models for specific tasks such as retrosynthesis (LocalRetro), reaction outcome prediction (LocalTransform), and atom-to-atom mapping (LocalMapper). These models, aligned with the intuition of chemists, demonstrate the effectiveness of incorporating reaction templates into deep learning frameworks.Looking toward the future, we believe that utilizing reaction templates to connect known chemical knowledge and AI models holds immense potential for various applications. Not only can this approach significantly benefit future AI models focused on challenging tasks like reaction mechanism labeling and prediction, but we anticipate it can also extend its reach to the realm of inorganic synthesis. By integrating synthesis knowledge, we can not only achieve improved performance but also enhance the interpretability of AI models, paving the way for further advancements in AI-powered chemical synthesis.

Leave No Photon Behind: Artificial Intelligence in Multiscale Physics of Photocatalyst and Photoreactor Design

Although solar fuels photocatalysis offers the promise of converting carbon dioxide directly with sunlight as commercially scalable solutions have remained elusive over the past few decades, despite significant advancements in photocatalysis band-gap engineering and atomic site activity. The primary challenge lies not in the discovery of new catalyst materials, which are abundant, but in overcoming the bottlenecks related to material-photoreactor synergy. These factors include achieving photogeneration and charge-carrier recombination at reactive sites, utilizing high mass transfer efficiency supports, maximizing solar collection, and achieving uniform light distribution within a reactor. Addressing this multi-dimensional problem necessitates harnessing machine learning techniques to analyze real-world data from photoreactors and material properties. In this perspective, the challenges are outlined associated with each bottleneck factor, review relevant data analysis studies, and assess the requirements for developing a comprehensive solution that can unlock the full potential of solar fuels photocatalysis technology. Physics-informed machine learning (or Physics Neural Networks) may be the key to advancing this important area from disparate data towards optimal reactor solutions.

Compositional transferability of deep potential in molten LiF-BeF2 and LaF3 mixtures: prediction of density, viscosity, and local structure

The accumulation of lanthanide fission products carries the risk of altering the structure and properties of the nuclear fuel carrier salt LiF-BeF2 (Flibe), thereby downgrading the operating efficiency and safety of the molten salt reactor. However, the condition-limited experimental measurements, spatiotemporal-limited first-principles calculations, and accuracy-limited classical dynamic simulations are unable to capture the precise local structure and reliable thermophysical properties of heterogeneous molten salts. Therefore, the deep potential (DP) of LaF3 and Flibe molten mixtures is developed here, and DP molecular dynamics simulations are performed to systemically study the densities, diffusion coefficients, viscosities, radial distribution functions and coordination numbers of multiple molten Flibe + xLaF3, the quantitative relationships between these properties and LaF3 concentration are investigated, and the potential structure-property relationships are analyzed. Eventually, the transferability of DP on molten Flibe + LaF3 with different formulations as well as the predictability of structures and properties are achieved at the nanometer spatial scale and the nanosecond timescale.

Physics-informed and data-driven discovery of governing equations for complex phenomena in heterogeneous media

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition software and hardware are providing vast amounts of data for various complex phenomena that occur in heterogeneous media, ranging from those in atmospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse multiscale and multiphysics phenomena that contain elements of stochasticity or heterogeneity, and to generate large volumes of numerical data for them. Thus, given a heterogeneous system with annealed or quenched disorder in which a complex phenomenon occurs, how should one analyze and model the system and phenomenon, explain the data, and make predictions for length and time scales much larger than those over which the data were collected? We divide such systems into three distinct classes. (i) Those for which the governing equations for the physical phenomena of interest, as well as data, are known, but solving the equations over large length scales and long times is very difficult. (ii) Those for which data are available, but the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on the data, or that the number of degrees of freedom of the system is so large that deriving the complete equations is very difficult, if not impossible, as a result of which one must develop the governing equations with reduced dimensionality. (iii) In the third class are systems for which large amounts of data are available, but the governing equations for the phenomena of interest are not known. Several classes of physics-informed and data-driven approaches for analyzing and modeling of the three classes of systems have been emerging, which are based on machine learning, symbolic regression, the Koopman operator, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation combined with a neural network, and stochastic optimization and analysis. This perspective describes such methods and the latest developments in this highly important and rapidly expanding area and discusses possible future directions.

Local-environment-guided selection of atomic structures for the development of machine-learning potentials

Machine learning potentials (MLPs) have attracted significant attention in computational chemistry and materials science due to their high accuracy and computational efficiency. The proper selection of atomic structures is crucial for developing reliable MLPs. Insufficient or redundant atomic structures can impede the training process and potentially result in a poor quality MLP. Here, we propose a local-environment-guided screening algorithm for efficient dataset selection in MLP development. The algorithm utilizes a local environment bank to store unique local environments of atoms. The dissimilarity between a particular local environment and those stored in the bank is evaluated using the Euclidean distance. A new structure is selected only if its local environment is significantly different from those already present in the bank. Consequently, the bank is then updated with all the new local environments found in the selected structure. To demonstrate the effectiveness of our algorithm, we applied it to select structures for a Ge system and a Pd13H2 particle system. The algorithm reduced the training data size by around 80% for both without compromising the performance of the MLP models. We verified that the results were independent of the selection and ordering of the initial structures. We also compared the performance of our method with the farthest point sampling algorithm, and the results show that our algorithm is superior in both robustness and computational efficiency. Furthermore, the generated local environment bank can be continuously updated and can potentially serve as a growing database of feature local environments, aiding in efficient dataset maintenance for constructing accurate MLPs.

Learning reduced-order models for cardiovascular simulations with graph neural networks

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.

Using Machine Learning to Predict Adverse Effects of Metallic Nanomaterials to Various Aquatic Organisms

The wide production and use of metallic nanomaterials (MNMs) leads to increased emissions into the aquatic environments and induces high potential risks. Experimentally evaluating the (eco)toxicity of MNMs is time-consuming and expensive due to the multiple environmental factors, the complexity of material properties, and the species diversity. Machine learning (ML) models provide an option to deal with heterogeneous data sets and complex relationships. The present study established an in silico model based on a machine learning properties-environmental conditions-multi species-toxicity prediction model (ML-PEMST) that can be applied to predict the toxicity of different MNMs toward multiple aquatic species. Feature importance and interaction analysis based on the random forest method indicated that exposure duration, illumination, primary size, and hydrodynamic diameter were the main factors affecting the ecotoxicity of MNMs to a variety of aquatic organisms. Illumination was demonstrated to have the most interaction with the other features. Moreover, incorporating additional detailed information on the ecological traits of the test species will allow us to further optimize and improve the predictive performance of the model. This study provides a new approach for ecotoxicity predictions for organisms in the aquatic environment and will help us to further explore exposure pathways and the risk assessment of MNMs.

Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of Fe-Al

We propose a machine-learning interatomic potential for multi-component magnetic materials. In this potential we consider magnetic moments as degrees of freedom (features) along with atomic positions, atomic types, and lattice vectors. We create a training set with constrained DFT (cDFT) that allows us to calculate energies of configurations with non-equilibrium (excited) magnetic moments and, thus, it is possible to construct the training set in a wide configuration space with great variety of non-equilibrium atomic positions, magnetic moments, and lattice vectors. Such a training set makes possible to fit reliable potentials that will allow us to predict properties of configurations in the excited states (including the ones with non-equilibrium magnetic moments). We verify the trained potentials on the system of bcc Fe-Al with different concentrations of Al and Fe and different ways Al and Fe atoms occupy the supercell sites. Here, we show that the formation energies, the equilibrium lattice parameters, and the total magnetic moments of the unit cell for different Fe-Al structures calculated with machine-learning potentials are in good correspondence with the ones obtained with DFT. We also demonstrate that the theoretical calculations conducted in this study qualitatively reproduce the experimentally-observed anomalous volume-composition dependence in the Fe-Al system.

Probing the Effect of Cuttings Particle Size on the Friction and Wear Mechanism at the Casing Friction Interface: A Molecular Dynamics Study

Cuttings particles of different sizes in the drilling fluid are the leading cause of wear at the casing and drill pipe joints, and diamond-like carbon (DLC) films have excellent research potential in reducing tool wear due to their ultra-low friction coefficient and high wear resistance. In this paper, a corresponding molecular dynamics model was developed using LAMMPS to investigate the effect of silica particles of different particle sizes on the friction and wear mechanisms of Fe/DLC friction pairs at the microscale. The results show that small cuttings particles in a dry environment are more likely to cause interface wear between the casing and drill pipe joint, while in a water environment, the opposite is true. The main reason is that small particles in a dry environment have smaller contact areas and greater indentation depth, leading to greater wear at the friction interface. The movement of water molecules in the water environment will promote the composite movement of large particles, thereby exacerbating the wear of the interface. Moreover, the relevant research results at the micro-scale indicate that DLC films can effectively reduce wear, which provides theoretical support for its application in drill pipe joints.

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.

Learning molecular dynamics: predicting the dynamics of glasses by a machine learning simulator

Many-body dynamics of atoms such as glass dynamics is generally governed by complex (and sometimes unknown) physics laws. This challenges the construction of atom dynamics simulations that both (i) capture the physics laws and (ii) run with little computation cost. Here, based on graph neural network (GNN), we introduce an observation-based graph network (OGN) framework to "bypass all physics laws" to simulate complex glass dynamics solely from their static structure. By taking the example of molecular dynamics (MD) simulations, we successfully apply the OGN to predict atom trajectories evolving up to a few hundred timesteps and ranging over different families of complex atomistic systems, which implies that the atom dynamics is largely encoded in their static structure in disordered phases and, furthermore, allows us to explore the capacity of OGN simulations that is potentially generic to many-body dynamics. Importantly, unlike traditional numerical simulations, the OGN simulations bypass the numerical constraint of small integration timestep by a multiplier of ≥5 to conserve energy and momentum until hundreds of timesteps, thus leapfrogging the execution speed of MD simulations for a modest timescale.

MLIP-3: Active learning on atomic environments with moment tensor potentials

Nowadays, academic research relies not only on sharing with the academic community the scientific results obtained by research groups while studying certain phenomena but also on sharing computer codes developed within the community. In the field of atomistic modeling, these were software packages for classical atomistic modeling, and later for quantum-mechanical modeling; currently, with the fast growth of the field of machine-learning potentials, the packages implement such potentials. In this paper, we present the MLIP-3 package for constructing moment tensor potentials and performing their active training. This package builds on the MLIP-2 package [Novikov et al., "The MLIP package: moment tensor potentials with MPI and active learning," Mach. Learn.: Sci. Technol., 2(2), 025002 (2020)], however, with a number of improvements, including active learning on atomic neighborhoods of a possibly large atomistic simulation.

Challenges for Kinetics Predictions via Neural Network Potentials: A Wilkinson's Catalyst Case

Ab initio kinetic studies are important to understand and design novel chemical reactions. While the Artificial Force Induced Reaction (AFIR) method provides a convenient and efficient framework for kinetic studies, accurate explorations of reaction path networks incur high computational costs. In this article, we are investigating the applicability of Neural Network Potentials (NNP) to accelerate such studies. For this purpose, we are reporting a novel theoretical study of ethylene hydrogenation with a transition metal complex inspired by Wilkinson's catalyst, using the AFIR method. The resulting reaction path network was analyzed by the Generative Topographic Mapping method. The network's geometries were then used to train a state-of-the-art NNP model, to replace expensive ab initio calculations with fast NNP predictions during the search. This procedure was applied to run the first NNP-powered reaction path network exploration using the AFIR method. We discovered that such explorations are particularly challenging for general purpose NNP models, and we identified the underlying limitations. In addition, we are proposing to overcome these challenges by complementing NNP models with fast semiempirical predictions. The proposed solution offers a generally applicable framework, laying the foundations to further accelerate ab initio kinetic studies with Machine Learning Force Fields, and ultimately explore larger systems that are currently inaccessible.

Deep Learning Accelerated Design of Mechanically Efficient Architected Materials

Lattice structures are known to have high performance-to-weight ratios because of their highly efficient material distribution in a given volume. However, their inherently large void fraction leads to low mechanical properties compared to the base material, high anisotropy, and brittleness. Most works to date have focused on modifying the spatial arrangement of beam elements to overcome these limitations, but only simple beam geometries are adopted due to the infinitely large design space associated with probing and varying beam shapes. Herein, we present an approach to enhance the elastic modulus, strength, and toughness of lattice structures with minimal tradeoffs by optimizing the shape of beam elements for a suite of lattice structures. A generative deep learning-based approach is employed, which leverages the fast inference of neural networks to accelerate the optimization process. Our optimized lattice structures possess superior stiffness (+59%), strength (+49%), toughness (+106%), and isotropy (+645%) compared to benchmark lattices consisting of cylindrical beams. We fabricate our lattice designs using additive manufacturing to validate the optimization approach; experimental and simulation results show good agreement. Remarkable improvement in mechanical properties is shown to be the effect of distributed stress fields and deformation modes subject to beam shape and lattice type.

A neural network based global traveltime function (GlobeNN)

Global traveltime modeling is an essential component of modern seismological studies with a whole gamut of applications ranging from earthquake source localization to seismic velocity inversion. Emerging acquisition technologies like distributed acoustic sensing (DAS) promise a new era of seismological discovery by allowing a high-density of seismic observations. Conventional traveltime computation algorithms are unable to handle virtually millions of receivers made available by DAS arrays. Therefore, we develop GlobeNN-a neural network based traveltime function that can provide seismic traveltimes obtained from the cached realistic 3-D Earth model. We train a neural network to estimate the traveltime between any two points in the global mantle Earth model by imposing the validity of the eikonal equation through the loss function. The traveltime gradients in the loss function are computed efficiently using automatic differentiation, while the P-wave velocity is obtained from the vertically polarized P-wave velocity of the GLAD-M25 model. The network is trained using a random selection of source and receiver pairs from within the computational domain. Once trained, the neural network produces traveltimes rapidly at the global scale through a single evaluation of the network. As a byproduct of the training process, we obtain a neural network that learns the underlying velocity model and, therefore, can be used as an efficient storage mechanism for the huge 3-D Earth velocity model. These exciting features make our proposed neural network based global traveltime computation method an indispensable tool for the next generation of seismological advances.

An Efficient Way to Model Complex Iron Carbides: A Benchmark Study of DFTB2 against DFT

Iron carbides have attracted increasing attention in recent years due to their enormous potential in catalytic fields, such as Fischer-Tropsch synthesis and the growth of carbon nanotubes. Theoretical calculations can provide a more thorough understanding of these reactions at the atomic scale. However, due to the extreme complexity of the active phases and surface structures of iron carbides at the operando conditions, calculations based on density functional theory (DFT) are too costly for realistically large models of iron carbide particles. Therefore, a cheap and efficient quantum mechanical simulation method with accuracy comparable to DFT is desired. In this work, we adopt the spin-polarized self-consistent charge density functional tight-binding (DFTB2) method for iron carbides by reparametrization of the repulsive part of the Fe-C interactions. To assess the performance of the improved parameters, the structural and electronic properties of iron carbide bulks and clusters obtained with DFTB2 method are compared with the previous experimental values and the results obtained with DFT approach. Calculated lattice parameters and density of states are close to DFT predictions. The benchmark results show that the proposed parametrization of Fe-C interactions provides transferable and balanced description of iron carbide systems. Therefore, spin-polarized DFTB2 is valued as an efficient and reliable method for the description of iron carbide systems.

Development of Deep Potentials of Molten MgCl2-NaCl and MgCl2-KCl Salts Driven by Machine Learning

Molten MgCl2-based chlorides have emerged as potential thermal storage and heat transfer materials due to high thermal stabilities and lower costs. In this work, deep potential molecular dynamics (DPMD) simulations by a method combination of the first principle, classical molecular dynamics, and machine learning are performed to systemically study the relationships of structures and thermophysical properties of molten MgCl2-NaCl (MN) and MgCl2-KCl (MK) eutectic salts at the temperature range of 800-1000 K. The densities, radial distribution functions, coordination numbers, potential mean forces, specific heat capacities, viscosities, and thermal conductivities of these two chlorides are successfully reproduced under extended temperatures by DPMD with a larger size (5.2 nm) and longer timescale (5 ns). It is concluded that the higher specific heat capacity of molten MK is originated from the strong potential mean force of Mg-Cl bonds, whereas the molten MN performs better in heat transfer due to the larger thermal conductivity and lower viscosity, attributed to the weak interaction between Mg and Cl ions. Innovatively, the plausibility and reliability of microscopic structures and macroscopic properties for molten MN and MK verify the extensibilities of these two deep potentials in temperatures, and these DPMD results also provide detailed technical parameters to the simulations of other formulated MN and MK salts.

Accelerating the design of compositionally complex materials via physics-informed artificial intelligence

The chemical space for designing materials is practically infinite. This makes disruptive progress by traditional physics-based modeling alone challenging. Yet, training data for identifying composition-structure-property relations by artificial intelligence are sparse. We discuss opportunities to discover new chemically complex materials by hybrid methods where physics laws are combined with artificial intelligence.

Graph Neural Tree: A novel and interpretable deep learning-based framework for accurate molecular property predictions

Determining various properties of molecules is a critical step in drug discovery. Recently, with the improvement of large heterogeneous datasets and the development of deep learning approaches, more and more scientists have turned their attention to neural network-based virtual preliminary screening to reduce the time and monetary cost of drug discovery. However, the poor interpretability of deep learning masks causality, so models' conclusions are often beyond the comprehension of human users, which reduces the credibility of the model and makes it difficult for chemists to further narrow the huge chemical space based on models' results. Thus, this study develops a novel framework consisting of Graph Neural Networks for feature extraction, Curriculum-Based Learning Strategies for optimization, and a Learning Binary Neural Tree (LBNT) for prediction, to improve the performance of neural networks and reveal their decision-making process to chemists. The framework encodes molecular graph data with graph neural networks (GNNs), then retrains the encoder with curriculum-based learning strategies to reduce uncertainty and improve accuracy, and finally uses LBNT as the predictor, which joint retrains with the encoder after independently training, for prediction and visualization. The framework is validated on the public datasets and compared to single GNNs with normal training strategies as well as GNN encoders with common machine learning predictors instead of the LBNT predictor. The result reveals that the proposed framework enhances the point prediction accuracy of the completely trained GNN and reduces its uncertainty through curriculum-based learning, and further improves the accuracy by combining LBNT. Besides, compared with common machine learning tools, the LBNT predictor generally has the best performance because of joint retraining with the GNN encoder. The decision-making process of LBNT is also better and easier to explain than that of other models.

Recent advances in density functional theory approach for optoelectronics properties of graphene

Graphene has received tremendous attention among diverse 2D materials because of its remarkable properties. Its emergence over the last two decades gave a new and distinct dynamic to the study of materials, with several research projects focusing on exploiting its intrinsic properties for optoelectronic devices. This review provides a comprehensive overview of several published articles based on density functional theory and recently introduced machine learning approaches applied to study the electronic and optical properties of graphene. A comprehensive catalogue of the bond lengths, band gaps, and formation energies of various doped graphene systems that determine thermodynamic stability was reported in the literature. In these studies, the peculiarity of the obtained results reported is consequent on the nature and type of the dopants, the choice of the XC functionals, the basis set, and the wrong input parameters. The different density functional theory models, as well as the strengths and uncertainties of the ML potentials employed in the machine learning approach to enhance the prediction models for graphene, were elucidated. Lastly, the thermal properties, modelling of graphene heterostructures, the superconducting behaviour of graphene, and optimization of the DFT models are grey areas that future studies should explore in enhancing its unique potential. Therefore, the identified future trends and knowledge gaps have a prospect in both academia and industry to design future and reliable optoelectronic devices.

Accessing the thermal conductivities of Sb2Te3 and Bi2Te3/Sb2Te3 superlattices by molecular dynamics simulations with a deep neural network potential

Phonon thermal transport is a key feature for the operation of thermoelectric materials, but it is challenging to accurately calculate the thermal conductivity of materials with strong anharmonicity or large cells. In this work, a deep neural network potential (NNP) is developed using a dataset based on density functional theory (DFT) and applied to describe the lattice dynamics of Sb₂Te₃ and Bi₂Te₃/Sb₂Te₃ superlattices. The lattice thermal conductivities of Sb₂Te₃ are first predicted using equilibrium molecular dynamics (EMD) simulations combined with an NNP and the results match well with experimental values. Then, through further exploration of weighted phase spaces and the Grüneisen parameter, we find that there is a stronger anharmonicity in the out-of-plane direction in Sb₂Te₃, which is the reason why the thermal conductivities are overestimated more in the out-of-plane direction than in the in-plane direction by solving the phonon Boltzmann transport equation (BTE) with only three-phonon scattering processes being considered. More importantly, the lattice thermal conductivities of Bi₂Te₃/Sb₂Te₃ superlattices with different periods are accurately predicted using non-equilibrium molecular dynamics (NEMD) simulations together with an NNP, which serves as a good example to explore the thermal transport physics of superlattices using a deep neural network potential.

Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process, effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems─all of high value to the FF community─but also the simple inclusion of further physical knowledge, such as higher-order information (e.g., Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.

Modeling Chemical Reactions in Alkali Carbonate-Hydroxide Electrolytes with Deep Learning Potentials

We developed a deep potential machine learning model for simulations of chemical reactions in molten alkali carbonate-hydroxide electrolyte containing dissolved CO₂, using an active learning procedure. We tested the deep neural network (DNN) potential and training procedure against reaction kinetics, chemical composition, and diffusion coefficients obtained from density functional theory (DFT) molecular dynamics calculations. The DNN potential was found to match DFT results for the structural, transport, and short-time chemical reactions in the melt. Using the DNN potential, we extended the time scales of observation to 2 ns in systems containing thousands of atoms, while preserving quantum chemical accuracy. This allowed us to reach chemical equilibrium with respect to several chemical species in the melt. The approach can be generalized for a broad spectrum of chemically reactive systems.

Machine Learning Accelerated Discovery of Promising Thermal Energy Storage Materials with High Heat Capacity

Thermal energy storage offers numerous benefits by reducing energy consumption and promoting the use of renewable energy sources. Thermal energy storage materials have been investigated for many decades with the aim of improving the overall efficiency of energy systems. However, finding solid materials that meet the requirement of high heat capacity has been a grand challenge for material scientists. Herewith, by training various machine learning models on 3377 high-quality data from full density functional theory (DFT) calculations, we efficiently search for potential materials with high heat capacity. We build four traditional machine learning models and two graph neural network models. Cross-comparison of the prediction performance and model accuracy was conducted among different models. The deeperGATGNN model exhibits high prediction accuracy and is used for predicting the heat capacity of 32,026 structures screened from the open quantum material database. We gain deep insight into the correlation between heat capacity and structure descriptors such as space group, prototype, lattice volume, atomic weight, etc. Twenty-two structures were predicted to possess high heat capacity, and the results were further validated with DFT calculations. We also identified one special structure, namely, MnIn₂Se₄, with space group no. 227 (Fd3̅m), that exhibits extremely high heat capacity, even higher than that of the Dulong-Petit limit at room temperature. This study paves the way for accelerating the discovery of novel thermal energy storage materials by combining machine learning with minimal DFT inquiry.

Machine Learning Methods for Multiscale Physics and Urban Engineering Problems

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where "multiscale" refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.

Accelerating the Layup Sequences Design of Composite Laminates via Theory-Guided Machine Learning Models

Experimental and numerical investigations are presented for a theory-guided machine learning (ML) model that combines the Hashin failure theory (HFT) and the classical lamination theory (CLT) to optimize and accelerate the design of composite laminates. A finite element simulation with the incorporation of the HFT and CLT were used to generate the training dataset. Instead of directly mapping the relationship between the ply angles of the laminate and its strength and stiffness, a multi-layer interconnected neural network (NN) system was built following the logical sequence of composite theories. With the forward prediction by the NN system and the inverse optimization by genetic algorithm (GA), a benchmark case of designing a composite tube subjected to the combined loads of bending and torsion was studied. The ML models successfully provided the optimal layup sequences and the required fiber modulus according to the preset design targets. Additionally, it shows that the machine learning models, with the guidance of composite theories, realize a faster optimization process and requires less training data than models with direct simple NNs. Such results imply the importance of domain knowledge in helping improve the ML applications in engineering problems.

Transition State Theory-Inspired Neural Network for Estimating the Viscosity of Deep Eutectic Solvents

The lack of accurate methods for predicting the viscosity of solvent materials, especially those with complex interactions, remains unresolved. Deep eutectic solvents (DESs), an emerging class of green solvents, have a severe lack of viscosity data, resulting in their application still staying at the stage of random trial and error, and it is difficult for them to be implemented on an industrial scale. In this work, we demonstrate the successful prediction of the viscosity of DESs based on the transition state theory-inspired neural network (TSTiNet). The TSTiNet adopts multilayer perceptron (MLP) for the transition state theory-inspired equation (TSTiEq) parameters calculation and verification using the most comprehensive DESs viscosity data set to date. For the energy parameters of the TSTiEq, the constant assumption and the fast iteration with the help of MLP can allow TSTiNet to achieve the best performance (the average absolute relative deviation on the test set of 6.84% and R ² of 0.9805). Compared with the traditional machine learning methods, the TSTiNet has better generalization ability and dramatically reduces the maximum relative deviation of prediction under the constraints of the thermodynamic formulation. It requires only the structural information on DESs and is the most accurate and reliable model available for DESs viscosity prediction.

Inverse Design for Coating Parameters in Nano-Film Growth Based on Deep Learning Neural Network and Particle Swarm Optimization Algorithm

The NN (neural network)-PSO (particle swarm optimization) method is demonstrated to be able to inversely extract the coating parameters for the multilayer nano-films through a simulation case and two experimental cases to verify its accuracy and robustness. In the simulation case, the relative error (RE) between the average layer values and the original one was less than 3.45% for 50 inverse designs. In the experimental anti-reflection (AR) coating case, the mean thickness values of the inverse design results had a RE of around 5.05%, and in the Bragg reflector case, the RE was less than 1.03% for the repeated inverse simulations. The method can also be used to solve the single-solution problem of a tandem neural network in the inverse process.

Machine Learning for Electrocatalyst and Photocatalyst Design and Discovery

Electrocatalysts and photocatalysts are key to a sustainable future, generating clean fuels, reducing the impact of global warming, and providing solutions to environmental pollution. Improved processes for catalyst design and a better understanding of electro/photocatalytic processes are essential for improving catalyst effectiveness. Recent advances in data science and artificial intelligence have great potential to accelerate electrocatalysis and photocatalysis research, particularly the rapid exploration of large materials chemistry spaces through machine learning. Here a comprehensive introduction to, and critical review of, machine learning techniques used in electrocatalysis and photocatalysis research are provided. Sources of electro/photocatalyst data and current approaches to representing these materials by mathematical features are described, the most commonly used machine learning methods summarized, and the quality and utility of electro/photocatalyst models evaluated. Illustrations of how machine learning models are applied to novel electro/photocatalyst discovery and used to elucidate electrocatalytic or photocatalytic reaction mechanisms are provided. The review offers a guide for materials scientists on the selection of machine learning methods for electrocatalysis and photocatalysis research. The application of machine learning to catalysis science represents a paradigm shift in the way advanced, next-generation catalysts will be designed and synthesized.

Machine Learning-Based Modeling of High-Pressure phase diagrams: Anomalousmelting of Rb

Modeling of phase diagrams and in particular the anomalous reentrant melting curves of thealkali metals is an open challenge for interatomic potentials. Machine learning-based interatomicpotentials have shown promise in overcoming this challenge, unlike earlier embedded atom-basedapproaches. We introduce a relatively simple and cheap approach to develop, train, and validate aneural network-based, wide-ranging interatomic potential transferable across both temperature andpressure. This approach is based on training the potential at high pressures only in the liquid phaseand on validating its transferability on the relatively easy-to-calculate cold compression curve. Ourapproach is demonstrated on the phase diagram of Rb for which we reproduce the cold compressioncurve over the Rb-I (BCC), Rb-II (FCC), and Rb-V (tI4) phases, followed by the high-pressuremelting curve including the re-entry after the maximum and then the minimum at the triple liquid-FCC-BCC point. Furthermore, our potential is able to partially capture even the very recentlyreported liquid-liquid transition in Rb, indicating the utility of machine learning-based potentials.

Machine learning the metastable phase diagram of covalently bonded carbon

Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct "metastable" phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n-diamond as a cubic-analog of diaphite-like lonsdaelite phase.

Machine learning accelerated random structure searching: Application to yttrium superhydrides

The search for new superhydrides, promising materials for both hydrogen storage and high temperature superconductivity, made great progress, thanks to atomistic simulations and Crystal Structure Prediction (CSP) algorithms. When they are combined with Density Functional Theory (DFT), these methods are highly reliable and often match a great part of the experimental results. However, systems of increasing complexity (number of atoms and chemical species) become rapidly challenging as the number of minima to explore grows exponentially with the number of degrees of freedom in the simulation cell. An efficient sampling strategy preserving a sustainable computational cost then remains to be found. We propose such a strategy based on an active-learning process where machine learning potentials and DFT simulations are jointly used, opening the way to the discovery of complex structures. As a proof of concept, this method is applied to the exploration of tin crystal structures under various pressures. We showed that the α phase, not included in the learning process, is correctly retrieved, despite its singular nature of bonding. Moreover, all the expected phases are correctly predicted under pressure (20 and 100 GPa), suggesting the high transferability of our approach. The method has then been applied to the search of yttrium superhydrides (YH x) crystal structures under pressure. The YH6 structure of space group Im-3m is successfully retrieved. However, the exploration of more complex systems leads to the appearance of a large number of structures. The selection of the relevant ones to be included in the active learning process is performed through the analysis of atomic environments and the clustering algorithm. Finally, a metric involving a distance based on x-ray spectra is introduced, which guides the structural search toward experimentally relevant structures. The global process (active-learning and new selection methods) is finally considered to explore more complex and unknown YH x phases, unreachable by former CSP algorithms. New complex phases are found, demonstrating the ability of our approach to push back the exponential wall of complexity related to CSP.

Multi-task graph neural networks for simultaneous prediction of global and atomic properties in ferromagnetic systems *

We introduce a multi-tasking graph convolutional neural network, HydraGNN, to simultaneously predict both global and atomic physical properties and demonstrate with ferromagnetic materials. We train HydraGNN on an open-source ab initio density functional theory (DFT) dataset for iron-platinum with a fixed body centered tetragonal lattice structure and fixed volume to simultaneously predict the mixing enthalpy (a global feature of the system), the atomic charge transfer, and the atomic magnetic moment across configurations that span the entire compositional range. By taking advantage of underlying physical correlations between material properties, multi-task learning (MTL) with HydraGNN provides effective training even with modest amounts of data. Moreover, this is achieved with just one architecture instead of three, as required by single-task learning (STL). The first convolutional layers of the HydraGNN architecture are shared by all learning tasks and extract features common to all material properties. The following layers discriminate the features of the different properties, the results of which are fed to the separate heads of the final layer to produce predictions. Numerical results show that HydraGNN effectively captures the relation between the configurational entropy and the material properties over the entire compositional range. Overall, the accuracy of simultaneous MTL predictions is comparable to the accuracy of the STL predictions. In addition, the computational cost of training HydraGNN for MTL is much lower than the original DFT calculations and also lower than training separate STL models for each property.

Thermal remote sensing over heterogeneous urban and suburban landscapes using sensor-driven super-resolution

Thermal remote sensing is an important tool for monitoring regional climate and environment, including urban heat islands. However, it suffers from a relatively lower spatial resolution compared to optical remote sensing. To improve the spatial resolution, various “data-driven” image processing techniques (pan-sharpening, kernel-driven methods, and machine learning) have been developed in the previous decades. Such empirical super-resolution methods create visually appealing thermal images; however, they may sacrifice radiometric consistency because they are not necessarily sensitive to specific sensor features. In this paper, we evaluated a “sensor-driven” super-resolution approach that explicitly considers the sensor blurring process, to ensure radiometric consistency with the original thermal image during high-resolution thermal image retrieval. The sensor-driven algorithm was applied to a cloud-free Moderate Resolution Imaging Spectroradiometer (MODIS) scene of heterogeneous urban and suburban landscape that included built-up areas, low mountains with a forest, a lake, croplands, and river channels. Validation against the reference high-resolution thermal image obtained by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) shows that the sensor-driven algorithm can downscale the MODIS image to 250-m resolution, while maintaining a high statistical consistency with the original MODIS and ASTER images. Part of our algorithm, such as radiometric offset correction based on the Mahalanobis distance, may be integrated with other existing approaches in the future.

PIGNet: a physics-informed deep learning model toward generalized drug-target interaction predictions

Recently, deep neural network (DNN)-based drug-target interaction (DTI) models were highlighted for their high accuracy with affordable computational costs. Yet, the models' insufficient generalization remains a challenging problem in the practice of in silico drug discovery. We propose two key strategies to enhance generalization in the DTI model. The first is to predict the atom-atom pairwise interactions via physics-informed equations parameterized with neural networks and provides the total binding affinity of a protein-ligand complex as their sum. We further improved the model generalization by augmenting a broader range of binding poses and ligands to training data. We validated our model, PIGNet, in the comparative assessment of scoring functions (CASF) 2016, demonstrating the outperforming docking and screening powers than previous methods. Our physics-informing strategy also enables the interpretation of predicted affinities by visualizing the contribution of ligand substructures, providing insights for further ligand optimization.

A Preliminary Study on the Resolution of Electro-Thermal Multi-Physics Coupling Problem Using Physics-Informed Neural Network (PINN)

The problem of electro-thermal coupling is widely present in the integrated circuit (IC). The accuracy and efficiency of traditional solution methods, such as the finite element method (FEM), are tightly related to the quality and density of mesh construction. Recently, PINN (physics-informed neural network) was proposed as a method for solving differential equations. This method is mesh free and generalizes the process of solving PDEs regardless of the equations’ structure. Therefore, an experiment is conducted to explore the feasibility of PINN in solving electro-thermal coupling problems, which include the electrokinetic field and steady-state thermal field. We utilize two neural networks in the form of sequential training to approximate the electric field and the thermal field, respectively. The experimental results show that PINN provides good accuracy in solving electro-thermal coupling problems.