On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it
University of the Basque Country (UPV/EHU)（巴斯克地区大学）；BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）；IKERBASQUE, Basque Foundation for Science（巴斯克科学基金会）；Zienkiewicz Centre for Computational Engineering (ZCCE), Swansea University（斯旺西大学齐恩基维茨计算工程中心）；BMW Group（宝马集团）
Andrea Bonfanti, Roberto Santana, Marco Ellero, Babak Gholami
Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we perform an empirical analysis of the behavior of PINN predictions outside their training domain. The primary goal is to investigate the scenarios in which a PINN can provide consistent predictions outside the training area. Thereinafter, we assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction. The results obtained in this study returns insightful and at times counterintuitive perspectives which can be highly relevant for architectures which combines PINNs with domain decomposition and/or adaptive training strategies.
Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scattering
Mathematical Applications in Science and Engineering Research Group, School of Applied Sciences and Engineering, Universidad EAFIT, Medellín, Colombia（数学应用科学与工程研究组，应用科学与工程学院，埃法特大学，麦德林，哥伦比亚）；Nature and Cities Research Group, School of Applied Sciences and Engineering, Universidad EAFIT, Medellín, Colombia（自然与城市研究组，应用科学与工程学院，埃法特大学，麦德林，哥伦比亚）
LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks
Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子与生物光子重点实验室，物理学院，长春理工大学）；Faculty of Chinese Medicine, Macau University of Science and Technology（澳门科技大学中医药学院）
Physics-Informed Neural Network Frameworks for the Analysis of Engineering and Biological Dynamical Systems Governed by Ordinary Differential Equations
Siena Heights University（锡耶纳高地大学）；Wayne State University（韦恩州立大学）
CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations
Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）；Beijing Normal University（北京师范大学）；Guangzhou Nanfang College（广州南方学院）；Louisiana State University（路易斯安那州立大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
A Rapid Physics-Informed Machine Learning Framework Based on Extreme Learning Machine for Inverse Stefan Problems
School of Qilu Transportation, Shandong University（山东大学齐鲁交通学院）；School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences)（齐鲁工业大学（山东省科学院）机械工程学院）
Solving stiff dark matter equations via Jacobian Normalization with Physics-Informed Neural Networks
Departamento de Física and CFTP Instituto Superior Técnico, Universidade de Lisboa（物理系和CFTP理工学院，里斯本大学）；Institute of Experimental and Applied Physics, Czech Technical University in Prague（实验与应用物理研究所，布拉格捷克技术大学）
CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries
Tsinghua University（清华大学）；Massachusetts Institute of Technology（麻省理工学院）；KU Leuven（荷语鲁汶大学）
Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks
Institute for Mathematics and Computer-Based Simulation (IMCS), University of the Bundeswehr Munich（慕尼黑联邦国防军大学数学与计算机模拟研究所）；Institute for the Protection of Terrestrial Infrastructures, German Aerospace Center (DLR)（德国航空航天中心陆地基础设施保护研究所）
Adaptive Physics-Informed Neural Networks with Multi-Category Feature Engineering for Hydrogen Sorption Prediction in Clays, Shales, and Coals
Faculty of Mathematics & Natural Sciences, University of Oslo（数学与自然科学学院，奥斯陆大学）；SINTEF Industry, Applied Geoscience Department（SINTEF工业公司，应用地球科学部门）；College of Geosciences, China University of Petroleum（地质科学学院，中国石油大学）
Discovering Physics-Informed Neural Networks Model for Solving Partial Differential Equations through Evolutionary Computation
National Engineering Laboratory for Big Data Analysis and Applications, Peking University（北京大学大数据分析与应用国家工程实验室）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；PKU-Changsha Institute for Computing and Digital Economy（北京大学长沙计算与数字经济研究院）
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
National University of Singapore（新加坡国立大学）；Worcester Polytechnic Institute（伍斯特理工学院）；Brown University（布朗大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
本文将 MC-fPINN 扩展为 MC-tfPINN，并用一维 Gaussian 求积替代 Monte Carlo 采样，在高达 100,000 维的分数阶与缓增分数阶 PDE 正、反问题中提升了精度和收敛速度。
Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture
Department of Geophysics, Colorado School of Mines（地质学系，科罗拉多矿业学院）；Department of Energy Science and Engineering, Stanford University（能源科学与工程系，斯坦福大学）；Department of Petroleum Engineering, Colorado School of Mines（石油工程系，科罗拉多矿业学院）
Model Based and Physics Informed Deep Learning Neural Network Structures
International Science Consulting and Training (ISCT)（国际科学咨询与培训（ISCT））；Zhejiang Shangfeng special blower company（浙江上风特种风机有限公司）；Central South University（中南大学）；Khalifa University（哈利法大学）；State Key Laboratory of Airliner Integration Technology and Flight Simulation（客机集成技术与飞行模拟国家重点实验室）
Bayesian Reasoning for Physics Informed Neural Networks
Institute for Theoretical Physics, University of Wroc aw（沃拉夫大学理论物理研究所）；Institute of Low Temperature and Structure Research（低温与结构研究所）；Polish Academy of Sciences（波兰科学院）
Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Field Theory Perspective
School of Computational Sciences（计算科学学院）；Korea Institute for Advanced Study（韩国高级研究院）；Department of Mathematical Science（数学科学系）；Seoul National University（首尔国立大学）
SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations
An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks
Department of Digital Industry Technologies, School of Science, National and Kapodistrian University of Athens（数字产业技术系，科学学院，国家与卡布利安大学）；Research Center for Astronomy and Applied Mathematics, Academy of Athens（天文与应用数学研究所，雅典学院）
Multi-level datasets training method in Physics-Informed Neural Networks
Department of Power Mechanical Engineering, National Tsing Hua University（国家交通大学机械工程系）；Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR)（高性能计算研究所，科技研究局（A*STAR））
