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Modeling unsteady, fast transient, and advection-dominated physics problems is a pressing challenge for physics-aware deep learning (PADL). The physics of complex systems is governed by large systems of partial differential equations (PDEs) and ancillary constitutive models with nonlinear structures, as well as evolving state fields exhibiting sharp gradients and rapidly deforming material interfaces. Here, we investigate an inductive bias approach that is versatile and generalizable to model generic nonlinear field evolution problems. Our study focuses on the recent physics-aware recurrent convolutions (PARC), which incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We extend the capabilities of PARC to simulate unsteady, transient, and advection-dominant systems. The extended model, referred to as PARCv2, is equipped with differential operators to model advection-reaction-diffusion equations, as well as a hybrid integral solver for stable, long-time predictions. PARCv2 is tested on both standard benchmark problems in fluid dynamics, namely Burgers and Navier-Stokes equations, and then applied to more complex shock-induced reaction problems in energetic materials. We evaluate the behavior of PARCv2 in comparison to other physics-informed and learning bias models and demonstrate its potential to model unsteady and advection-dominant dynamics regimes. 

Abstract Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future. 

Complex spin textures in itinerant electron magnets hold promises for next-generation memory and information technology. The long-ranged and often frustrated electron-mediated spin interactions in these materials give rise to intriguing localized spin structures such as skyrmions. Yet, simulations of magnetization dynamics for such itinerant magnets are computationally difficult due to the need for repeated solutions to the electronic structure problems. We present a convolutional neural network (CNN) model to accurately and efficiently predict the electron-induced magnetic torques acting on local spins. Importantly, as the convolutional operations with a fixed kernel (receptive field) size naturally take advantage of the locality principle for many-electron systems, CNNs offer a scalable machine learning approach to spin dynamics. We apply our approach to enable large-scale dynamical simulations of skyrmion phases in itinerant spin systems. By incorporating the CNN model into Landau-Lifshitz-Gilbert dynamics, our simulations successfully reproduce the relaxation process of the skyrmion phase and stabilize a skyrmion lattice in larger systems. The CNN model also allows us to compute the effective receptive fields, thus providing a systematic and unbiased method for determining the locality of the original electron models. 

Deep learning can learn the complex physics of energetic materials. 

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