Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical systems that can be well described by models with quadratic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto quadratic models. The proposed regularizer is physics informed in the sense that it penalizes quadratic terms with large norms and so explicitly leverages the quadratic model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in the linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization or Tikhonov regularization leads to models that are unstable.
Data-Informed Mathematical Characterization of Absorption Properties in Artificial and Natural Porous Materials
CNR National Research Council of Italy - Institute for Applied Mathematics “M. Picone”（意大利国家研究委员会应用数学研究所“M. Picone”）；Sapienza, University of Rome - Department of Earth Sciences（罗马大学地球科学系）
Physics informed learning of orthogonal features with applications in solving partial differential equations
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen Research Institute of Big Data（深圳高等研究院工业与应用数学国际中心）；Shenzhen Loop Area Institute（深圳河套学院）
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）
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
Massachusetts Institute of Technology（麻省理工学院）；University of California San Diego（加州大学圣地亚哥分校）；New York University（纽约大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Deep regularization networks for inverse problems with noisy operators
1.25mm 1 Department of Civil, Environmental \& Architectural Engineering, University of Colorado Boulder, USA；1mm 2 Department of Applied Mathematics, University of Colorado Boulder, USA
CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networks
Stony Brook University（石溪大学）；Center of Excellence in Wireless and Information Technology（无线与信息技术卓越中心）；Institute for Advanced Computational Science（高级计算科学研究所）
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）
Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Bias
Department of Computer Science and Engineering（计算机科学与工程系）；The Hong Kong University of Science and Technology（香港科学与技术大学）；School of Mathematical Sciences（数学科学学院）；Peking University（北京大学）；Department of Computer Science（计算机科学系）；University of Warwick（沃里克大学）；Industrial Engineering & Management Sciences（工业工程与管理科学）；Northwestern University（西北大学）
