Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. Additionally, purely data-based models often require large amounts of data and are often difficult to interpret. In this paper, we present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. This new approach directly incorporates the equations of motion originating from the Lagrange Mechanics into a deep neural network structure. Thus, we can integrate prior physics knowledge where it is available and use function approximation--e. g., neural networks--where it is not. The method is tested with a forward model of a real-world physical system with large uncertainties. The resulting model is accurate and data-efficient while ensuring physical plausibility. With this, we demonstrate a method that beneficially merges physical insight with real data. Our findings are of interest for model-based control and system identification of mechanical systems.
SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications
Department of Applied Mechanics（应用力学系）；Indian Institute of Technology Delhi（德里印度理工学院）；Institute of Structural Mechanics and Dynamics in Aerospace Engineering（航空航天工程中的结构力学与动力学研究所）；Faculty of Aerospace Engineering and Geodesy（航空航天工程与大地测量学系）；University of Stuttgart（斯图加特大学）；Experimental Hepatobiliary Surgery Group（肝胆外科实验小组）；Department of Hepatobiliary Surgery and Visceral Transplantation（肝胆外科与内脏移植部）；University of Leipzig Medical Center（莱比锡大学医学中心）；Department of Civil and Systems Engineering（土木与系统工程系）；Johns Hopkins University（约翰霍普金斯大学）；Data Science and AI Institute（数据科学与人工智能研究所）；Yardi School of Artificial Intelligence (YScAI)（Yardi人工智能学院（YScAI））
LT-PINN: Lagrangian Topology-conscious Physics-informed Neural Network for Boundary-focused Engineering Optimization
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China（土木与环境工程系，香港理工大学，香港，中国）；Research Institute for Sustainable Urban Development (RISUD), The Hong Kong Polytechnic University, Hong Kong, China（可持续城市发展研究院（RISUD），香港理工大学，香港，中国）；Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, China（机械工程系，香港理工大学，香港，中国）；School of Fashion and Textiles, The Hong Kong Polytechnic University, Hong Kong, China（时尚与纺织学院，香港理工大学，香港，中国）；Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China（机械工程系，香港大学，香港，中国）
Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks
College of Mechanics and Engineering Science, Hohai University（河海大学力学与工程科学学院）；China Three Gorges Corporation（中国长江三峡集团有限公司）；Cairo University（开罗大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
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）
Learning Fluid-Structure Interaction with Physics-Informed Machine Learning and Immersed Boundary Methods
Computational Science and Engineering Department, Informatics Institute Istanbul Technical University（信息学院伊斯坦布尔技术大学计算科学与工程系）；Scientific Computing, Rutherford Appleton Laboratory Science and Technology Facilities Council (STFC)（科学与技术设施理事会（STFC）科学计算部）
A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
University of British Columbia（不列颠哥伦比亚大学）；Broad Institute of MIT（MIT-哈佛Broad研究所）；University of Alberta（阿尔伯塔大学）；Alberta Machine Intelligence Institute（阿尔伯塔机器智能研究所）；Mila - Quebec AI Institute（魁北克AI研究所）
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
Brown University（布朗大学）；Technische Universität Ilmenau（伊尔默瑙工业大学）
Lagrangian neural networks for nonholonomic mechanics
Departamento de Matemática, Universidad Nacional del Sur（国家南方大学数学系）；Centro de Matemática de La Plata, Universidad Nacional de La Plata（拉普拉塔国立大学拉普拉塔数学中心）
Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation
MOX Laboratory, Department of Mathematics, Politecnico di Milano（米兰Politecnico大学数学系MOX实验室）；Division 2.2 Process Simulation, Bundesanstalt für Materialforschung und -prüfung (BAM)（材料研究所（BAM）第2.2过程模拟部）；Department of Mathematics, University of Trento（特伦托大学数学系）
