Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations
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）；University of Chinese Academy of Sciences（中国科学院大学）；Brown University（布朗大学）
Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan
备注：
25 pages, 17 figures
发表信息：
Journal of Computational Physics 505 (2024) 112917
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and continues training on the basis of the first subnetwork. Importantly, the IINN method does not require any additional data information including boundary conditions, apart from the given initial value. Corresponding theoretical guarantees are provided to demonstrate the effectiveness of our IINN method. The proposed IINN method is efficiently applied to learn some types of solutions in different nonlinear wave equations, including the one-dimensional (1D) nonlinear Schrödinger equations (NLS) equation (with and without potentials), the 1D saturable NLS equation with PT -symmetric optical lattices, the 1D focusing-defocusing coupled NLS equations, the KdV equation, the two-dimensional (2D) NLS equation with potentials, the 2D amended GP equation with a potential, the (2+1)-dimensional KP equation, and the 3D NLS equation with a potential. These applications serve as evidence for the efficacy of our method. Finally, by comparing with the traditional methods, we demonstrate the advantages of the proposed IINN method.
A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation
Department of Mathematics and the Institute for Scientific Computing and Applied Mathematics, Indiana University（数学系和科学计算与应用数学研究所，印第安纳大学）；Department of Mathematics and Cognitive Science Program, Indiana University（数学系和认知科学项目，印第安纳大学）
Simulating Three-dimensional Turbulence with Physics-informed Neural Networks
Institution for Foundation of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（机械工程与应用力学系，宾夕法尼亚大学）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（机械与航空航天工程学院，康奈尔大学）；Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory（先进计算、数学和数据部门，太平洋西北国家实验室）
Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifolds
Department of Bio-Functions and Systems Science（生物功能与系统科学系）；Graduate School of Bio-Applications and Systems Engineering（生物应用与系统工程研究生学校）；Department of Mathematics（数学系）；Faculty of Mathematics and Natural Sciences（数学与自然科学学院）；Universitas Padjadjaran（帕迪贾兰大学）；Department of Informatics（信息系）；Faculty of Science and Informatics（科学与信息学院）；Jenderal of Achmad Yani University（阿赫马德·亚尼大学）
Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis
George Mason University（乔治梅森大学）；National Institute of Natural Hazards, Ministry of Emergency Management（应急管理部国家自然灾害防治研究院）；Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences（中国科学院西北生态环境资源研究院）；École Nationale des Ponts et Chaussées（巴黎路桥学院）；Hebei University of Engineering（河北工程大学）；Zhejiang University of Technology（浙江工业大学）
Integrating Physics-Informed Neural Networks for Safe Reinforcement Learning in a 1-DoF Helicopter System
Josef Ressel Centre for Intelligent and Secure Industrial Automation, Salzburg University of Applied Sciences（约瑟夫·雷塞尔智能与安全工业自动化中心，萨尔茨堡应用科学大学）；Salzburg University of Applied Sciences（萨尔茨堡应用科学大学）；Paris Lodron University of Salzburg（萨尔茨堡帕里斯·洛德隆大学）
Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computing
University of Bristol, School of Computer Science（布里斯托大学计算机科学学院）；University of Bristol, School of Engineering Mathematics and Technology（布里斯托大学工程数学与技术学院）
MIXPINN: Mixed-Material Simulations by Physics-Informed Neural Network
Department of Computer Science, ETH Zurich（苏黎世联邦理工学院计算机科学系）；ROCS, Balgrist University Hospital, University of Zurich（苏黎世大学罗兹医学中心）；ETH AI Center, ETH Zürich（苏黎世联邦理工学院人工智能中心）
DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling
Department of Computer Science, School of Computing, National University of Singapore（新加坡国立大学计算机科学系）；School of Civil Engineering, Faculty of Engineering, The University of Sydney（悉尼大学土木工程学院）；Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学应用数学研究所）
Physics-Informed Neural Operators for Cardiac Electrophysiology
Department of Informatics, King’s College London, UK（信息学院，伦敦国王学院，英国）；Research Department of Digital Twins in Healthcare, King’s College London, UK（医疗数字孪生研究部，伦敦国王学院，英国）
Coarse Graining with Neural Operators for Simulating Chaotic Systems
Department of Computing and Mathematical Sciences, California Institute of Technology（计算与数学科学系，加利福尼亚理工学院）；NVIDIA Research（NVIDIA研究）；Graduate Aerospace Laboratories, California Institute of Technology（航空航天实验室，加利福尼亚理工学院）
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
Department of Mathematics and Computer Science, Eindhoven University of Technology（数学与计算机科学系，埃因霍温理工大学）；Atlantis project-team, Inria Research Center at Université Côte d'Azur（Atlantis项目组，法国国家信息与自动化技术研究院（Inria）在阿尔卑斯大学（Université Côte d'Azur）的研究中心）；MACARON project-team, Université de Strasbourg, CNRS, Inria, IRMA（MACARON项目组，斯特拉斯堡大学，法国国家科学研究中心（CNRS），法国国家信息与自动化技术研究院（Inria），IRMA）
Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks
Washington University in St. Louis（华盛顿大学圣路易斯分校）；University of Notre Dame（诺特大学）；Central South University（中南大学）；Stanford University（斯坦福大学）；New York University（纽约大学）
Deep Learning Alternatives of the Kolmogorov Superposition Theorem
Graduate Group in Applied Mathematics and Computational Science（应用数学与计算科学联合研究生组）；University of Pennsylvania（宾夕法尼亚大学）；Department of Mechanical Engineering & Applied Mechanics（机械工程与应用力学系）
Centre for Artificial Intelligence, University College London（人工智能研究中心，伦敦大学学院）；Heudiasyc Laboratory（Heudiasyc实验室）；Mila - Quebec AI Institute（魁北克人工智能研究所）
The improved backward compatible physics-informed neural networks for reducing error accumulation and applications in data-driven higher-order rogue waves
Solving Navier-Stokes Equations Using Data-free Physics-Informed Neural Networks With Hard Boundary Conditions
Indian Institute of Technology Patna（印度巴特那理工学院）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究特里凡得琅研究所）；Patna University（巴特那大学）
Ab initio simulations of the thermodynamic properties and phase transition of Fermi systems based on fictitious identical particles and physics-informed neural networks
