Characterizing possible failure modes in physics-informed neural networks
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Utah（犹他大学）；International Computer Science Institute（国际计算机科学研究所）
Aditi S. Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M. Kirby, Michael W. Mahoney
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use existing machine learning methodologies to train the model. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena for even slightly more complex problems. In particular, we analyze several distinct situations of widespread physical interest, including learning differential equations with convection, reaction, and diffusion operators. We provide evidence that the soft regularization in PINNs, which involves PDE-based differential operators, can introduce a number of subtle problems, including making the problem more ill-conditioned. Importantly, we show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize. We then describe two promising solutions to address these failure modes. The first approach is to use curriculum regularization, where the PINN's loss term starts from a simple PDE regularization, and becomes progressively more complex as the NN gets trained. The second approach is to pose the problem as a sequence-to-sequence learning task, rather than learning to predict the entire space-time at once. Extensive testing shows that we can achieve up to 1-2 orders of magnitude lower error with these methods as compared to regular PINN training.
Improved physics-informed neural network in mitigating gradient related failures
College of Applied Mathematics, Chengdu University of Information Technology（成都信息工程大学应用数学学院）；College of Mathematics, Sichuan University（四川大学数学学院）；School of Sciences, Southwest Petroleum University（西南石油大学理学院）
Seeing Structural Failure Before it Happens: An Image-Based Physics-Informed Neural Network (PINN) for Spaghetti Bridge Load Prediction
Department of Computer Science, National University of Computer and Emerging Sciences (FAST-NUCES)（计算机科学系，国立计算机与新兴科学大学（FAST-NUCES））；Department of Computer and Network Engineering, United Arab Emirates University (UAEU)（计算机与网络工程系，阿拉伯联合酋长国大学（UAEU））
Gryphon Center for Artificial Intelligence and Theoretical Sciences（格里芬人工智能与理论科学中心）；Georgia Institute of Technology（佐治亚理工学院）；University of Pennsylvania（宾夕法尼亚大学）
Parameterized Physics-informed Neural Networks for Parameterized PDEs
Yonsei University（延世大学）；Arizona State University（亚利桑那州立大学）；LG CNS；Texas A&M University-Commerce（德州农工大学Commerce分校）；Oregon State University（俄勒冈州立大学）；KAIST（韩国科学技术院）
Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks
College of Computer Science and Technology/Artificial Intelligence, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院/人工智能学院）；MIIT Key Laboratory of Pattern Analysis and Machine Intelligence（工业和信息化部模式分析与机器智能重点实验室）
WarpPINN: Cine-MR image registration with physics-informed neural networks
University of Bath（巴斯大学）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主大学）；Millennium Institute for Intelligent Healthcare Engineering（千年智能医疗工程研究所）；Pontificia Universidad Católica de Chile（智利天主大学）
Physics-Informed Machine Learning for Characterizing System Stability
School of Aerospace Engineering（航空航天工程学院）；AIAA Student Member（美国航空航天学会学生会员）；Schools of Aerospace Engineering & Computational Science and Engineering（航空航天工程与计算科学与工程学院）；AIAA Member（美国航空航天学会会员）
Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis
University of Maryland, College Park, MD 20742, United States（马里兰大学学院公园分校）；Florida Atlantic University, Boca Raton, FL 33431, United States（佛罗里达 Atlantic 大学）
Large Language Model-informed ECG Dual Attention Network for Heart Failure Risk Prediction
Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford（生物医学工程研究所，工程科学系，牛津大学）；Imperial College London（伦敦帝国学院）；University of Sheffield（谢菲尔德大学）；Novo Nordisk Research Centre Oxford (NNRCO)（牛津诺和硕研究中心（NNRCO））；Royal Society（皇家学会）
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）
