We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) [Raissi et al., J. Comput. Phys., 378:686--707, 2019] because the method parameterizes not only the solutions but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than existing methods in terms of the standard L2-norm metric.
Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks
National Center for Applied Mathematics, Tianjin University（天津大学应用数学中心）；School of Mechanical and Aerospace Engineering, Jilin University（吉林大学机械与 aerospace 工程学院）
xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning
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）
A Coupled Physics-Informed Neural Network for Greenhouse Climate State Reconstruction and Parameter Identification under Sparse Sensor Measurements
Centro de Modelamiento Matemático (CMM), University of Chile（智利大学数学建模中心）；College of Science, King Khalid University（哈立德国王大学理学院）；Presidency University（总统大学）
Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of Nitrogen Oxides
University of Southern California（南加州大学）；State Key Laboratory of Resources and Environmental Information System, Institute of Geographical Sciences and Natural Resources, Chinese Academy of Sciences（中国科学院地理科学与资源研究所资源与环境信息系统国家重点实验室）；Sonoma Technology, Inc.（索诺玛技术公司）；Susan and Henry Samueli College of Health Sciences, University of California, Irvine（加州大学欧文分校苏珊和亨利萨穆埃利健康科学学院）；Fielding School of Public Health, University of California, Los Angeles（加州大学洛杉矶分校菲尔丁公共卫生学院）；Goddard Space Flight Center, National Aeronautics and Space Administration（美国国家航空航天局戈达德太空飞行中心）；University of Toronto（多伦多大学）；Spatial Sciences Institute, University of Southern California（南加州大学空间科学学院）
The University of Arizona（亚利桑那大学）；Massachusetts Institute of Technology（麻省理工学院）
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning…
Towards Spatio-Temporal Extrapolation of Phase-Field Simulations with Convolution-Only Neural Networks
Sandia National Laboratories（桑迪亚国家实验室）；Lawrence Berkeley National Laboratory（伯克利劳伦斯国家实验室）；University of California, Berkeley（加州大学伯克利分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
University of Calgary（卡尔加里大学）；Carleton University（卡尔顿大学）
In this work, we present a deep neural network architecture that can efficiently approximate classical elasto-plastic constitutive relations. The network is enriched with crucial physics aspects of classical elasto-plasticity, including additive decomposition of strains into elastic and plastic parts, and nonlinear incremental elasticity. This leads to a Physics-Informed Neural Network (PINN) surrogate model named here as Elasto-Plastic Neural Network (EPNN). Detailed analyses show that embedding these physics into the architecture of the neural network facilitates a more efficient training of…
Lane Department of Computer Science and Electrical Engineering, West Virginia University（计算机科学与电气工程系，西弗吉尼亚大学）
Despite the relentless progress of deep learning models in analyzing the system conditions under cyber-physical events, their abilities are limited in the power system domain due to data availability issues, cost of data acquisition, and lack of interpretation and extrapolation for the data beyond the training windows. In addition, the integration of distributed energy resources (DERs) such as wind and solar generations increases the complexities and nonlinear nature of power systems. Therefore, an interpretable and reliable methodology is of utmost need to increase the confidence of power sys…
Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution
Tongji University, College of Civil Engineering（同济大学，土木工程学院）；Tongji University, State Key Laboratory of Disaster Reduction in Civil Engineering（同济大学，灾害防治工程重点实验室）
Hamburg University of Technology（汉堡工业大学）；Stanford University（斯坦福大学）；Brown University（布朗大学）
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and make decision around them. Neural networks are now consistently used as universal function approximators for data with underlying mechanisms that are incompletely understood or exceedingly complex. However, neural networks alone ignore the fundamental laws of physics and often fail to make plausible predictions. Here we integrate data, physics, and uncertai…
Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective
Cho Chun Shik Graduate School of Mobility（赵春植移动研究生院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Seoul National University（首尔大学）；Institute of Advanced Machines and Design（先进机械与设计研究所）；College of Information Sciences and Technology（信息科学与技术学院）；The Pennsylvania State University（宾夕法尼亚州立大学）；German Aerospace Center (DLR, Deutsches Zentrum für Luft- und Raumfahrt)（德国航空航天中心）
Investment professionals rely on extrapolating company revenue into the future (i.e. revenue forecast) to approximate the valuation of scaleups (private companies in a high-growth stage) and inform their investment decision. This task is manual and empirical, leaving the forecast quality heavily dependent on the investment professionals' experiences and insights. Furthermore, financial data on scaleups is typically proprietary, costly and scarce, ruling out the wide adoption of data-driven approaches. To this end, we propose a simulation-informed revenue extrapolation (SiRE) algorithm that gen…
LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE
Ocean College, Zhejiang University（浙江大学海洋学院）；Ocean Research Center of Zhoushan, Zhejiang University（浙江大学舟山海洋研究中心）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新研究院）
Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important role in many fields. However, PINN uses a fully connected network as its model, which has limited fitting ability and limited extrapolation ability in both time and space. In this paper, we propose PhyGNNet for solving partial differential equations on the basics of a graph neural network which consists of encoder, processer, and decoder blocks. In particul…
Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For example, the lack of accurate baseline models, high dimensionality, and complex multivariate partial differential equations (PDEs) pose significant difficulties in training and learning conventional data-driven algorithms. This paper explores a new framework, dubbed NeuralSI, for structural identification by augmenting PDEs that govern structural dynamics with …
Physics-informed reduced order model with conditional neural fields
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；University of Notre Dame（圣母大学）；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）
Knowledge Integration in Differentiable Models: A Comparative Study of Data-Driven, Soft-Constrained, and Hard-Constrained Paradigms for Identification and Control of the Single Machine Infinite Bus System
Korea University（高丽大学）；Hyundai Motor Company（现代汽车公司）
PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；School of Engineering Science, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）
Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data, especially in extrapolation tasks. To address these limitations, we propose Physics Informed Deep Kernel Learning (PI-DKL) that exploits physics knowledge represented by differential equations with latent sources. Specifically, we use the posterior function sample of the Gaussian process as the surrogate for the solution of the differential equation, and co…
tLaSDI: Thermodynamics-informed latent space dynamics identification
Korea Institute for Advanced Study (KIAS)（韩国高等研究院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Pohang University of Science and Technology (POSTECH)（浦项科技大学）
We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The network is used to simulate the dynamic behavior of physical quantities (i.e. saturation) subject to a set of governing laws (e.g. mass conservation) and corresponding boundary and initial conditions. A residual equation is formed from the governing partial-differential equation and used as part of the training. Derivatives of the estimated physical quantities are computed using automatic…
Least-Action-Guided Diffusion for Physical Extrapolation
College of Engineering, Peking University（北京大学工学院）；Ningbo Institute for Digital Twin, Eastern Institute of Technology（东方理工宁波数字孪生研究院）；Eastern Institute for Advanced Study, Eastern Institute of Technology（东方理工高等研究院）；Shenzhen Tenfong Technology Co., Ltd.（深圳腾方科技有限公司）；Mechanical Engineering, The Pennsylvania State University（宾夕法尼亚州立大学机械工程系）
