Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a least squares space-time control volume scheme, we circumvent issues particularly related to imposition of boundary conditions and conservation while reducing solution regularity requirements. Additionally, connections to classical finite volume methods allows application of biases toward entropy solutions and total variation diminishing properties. For inverse problems, we may impose further thermodynamic biases, allowing us to fit shock hydrodynamics models to molecular simulation of rarefied gases and metals. The resulting data-driven equations of state may be incorporated into traditional shock hydrodynamics codes.
A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocomposites
Institute of Structural Analysis, Leibniz Universität Hannover（莱布尼茨汉诺威大学结构分析研究所）；Department of Mechanical, Electrical and Chemical Engineering, Oslo Metropolitan University（奥斯陆城市大学机械、电气与化学工程系）；Institute of Lightweight Systems, Multifunctional Materials, DLR (German Aerospace Center)（德国航空航天中心轻量化系统与多功能材料研究所）
Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems
Ansys Inc.（安西斯公司）；North Carolina State University（北卡罗来纳州立大学）；Sandia National Laboratories（桑迪亚国家实验室）；Arizona State University（亚利桑那州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
On thermodynamically compatible finite volume schemes for continuum mechanics
本文对超定双曲型和双曲型相容偏微分方程组提出了一族新的半离散和全离散有限体积格式。在下文中，我们将这些方法称为HTC方案。特别是，我们认为欧拉方程的可压缩气体动力学，以及更复杂的Godunov-Peshkov-Romenski（GPR）模型的连续介质力学，其中，在适当的松弛源项的帮助下，能够描述非线性弹塑性固体在大变形以及粘性流体作为两个特殊情况下的一个更一般的一阶双曲模型的连续介质力学。本文提出的方案的主要新颖之处在于，我们解决的\textit{entropy inequality}作为一个主要的发展方程，而不是通常的总能量守恒律。相反，实现总能量守恒仅仅是所有其他方程的一个相容离散化的结果。为此，我们首先构建了一个离散的可压缩欧拉方程的框架，模仿连续框架Goddom的开创性论文\textit{An interesting class of quasilinear systems}的1961年\textit{exactly}在离散水平。在更一般的GPR模型，包括非保守产品的控制方程中的所有其他条款，明智地离散，以实现离散的热力学兼容性，与作为所有其他方程的直接后果的总能量密度的精确守恒。结果表明，本文提出的HTC格式在能量范数下是可证明的边缘稳定的，并且通过构造满足离散熵不等式。我们显示了一些计算结果与HTC计划在一个和两个空间维度，考虑流体限制以及固体限制的控制偏微分方程。
Structure-Informed Data-Driven Reduced-Order Modeling of Scalar Hyperbolic Conservation Laws via Kinetic Defect Measure
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与应用力学系）
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Center for Quantitative Biology, Center for Machine Learning Research, Peking University（北京大学定量生物学中心、机器学习研究中心）；Academy for Multidisciplinary Studies, Capital Normal University（首都师范大学跨学科研究院）；Beijing National Center for Applied Mathematics（北京应用数学中心）
Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
Division of Applied Mathematics, Linköping University（林雪平大学应用数学系）；Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）
Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems
Department of Mathematics, The Pennsylvania State University（数学系，宾夕法尼亚州立大学）；Department of Mathematics, The Hong Kong University of Science and Technology（数学系，香港科学与技术大学）；Department of Mathematics, University of South Carolina（数学系，南卡罗来纳大学）
GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale（建模工程风险与复杂性，南方高级学校）；Dept. of Electrical Engineering and Information Technology, University of Naples Federico II（电气工程与信息技术系，那不勒斯费德里科二世大学）；Institute of Science and Technology for Energy and Sustainable Mobility, Consiglio Nazionale delle Ricerche（能源与可持续交通科学与技术研究所，意大利国家研究委员会）
A thermodynamically compatible semi-implicit finite volume scheme for the compressible Euler equations
University of Trento（特伦托大学）；Southern University of Science and Technology（南方科技大学）；La Sapienza Università di Roma（罗马第一大学）；Université de Strasbourg（斯特拉斯堡大学）；Inria
CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains
Department of Aerospace Engineering, Sharif University of Technology（谢里夫理工大学航空航天工程系）
Weak and entropy physics-informed neural networks for conservation laws
Mohammed VI Polytechnic University（穆罕默德六世polytechnic大学）；LAGA, CNRS, UMR 7539, Université Sorbonne Paris Nord（索邦巴黎北大学LAGA实验室，法国国家科学研究中心）；Autorité de Sûreté Nucléaire et de Radioprotection (ASNR)（核安全与辐射防护管理局）；McGill University（麦吉尔大学）
Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
Mathematical Sciences Institute and France-Australia Mathematical Sciences and Interactions ANU-CNRS International Research Lab（数学科学研究所和法国-澳大利亚数学科学与互动 ANU-CNRS 国际研究实验室）
