A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters.
A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity
The University of New South Wales（新南威尔士大学）；Massachusetts Institute of Technology（麻省理工学院）；University of British Columbia（不列颠哥伦比亚大学）；Sharif University of Technology（谢里夫理工大学）
Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data
Department of Industrial and Systems Engineering, Texas A&M University（工业与系统工程系，德克萨斯大学阿马尔科分校）；Department of Mechanical Engineering, Texas A&M University（机械工程系，德克萨斯大学阿马尔科分校）
Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院数学科学系）；Department of Mathematics, Gyeongsang National University（庆尚国立大学数学系）；Department of Mathematics, Sungkyunkwan University（全州大学数学系）；Department of Electrical and Computer Engineering, Sungkyunkwan University（全州大学电子与计算机工程系）
SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling
Department of Mechanical Engineering, University of Wisconsin-Madison（威斯康星大学麦迪逊分校机械工程系）；Department of Mathematics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校数学系）；Department of Civil Engineering, Johns Hopkins University（约翰霍普金斯大学土木工程系）；Materials Physics and Applications Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室材料物理与应用 division）；Department of Materials Science and Engineering, University of Wisconsin-Madison（威斯康星大学麦迪逊分校材料科学与工程系）
Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?
Department of Radiophysics, University of Nizhny Novgorod（尼日尼诺夫戈罗德大学无线电物理系）；Huawei Nizhny Novgorod Research Center（华为尼日尼诺夫戈罗德研究中心）；Skolkovo Institute of Science and Technology（斯克尔科沃科学技术研究院）
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）
Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging
Beijing University of Technology（北京工业大学）；Dalian University of Technology（大连理工大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）；Tongji University（同济大学）；Bauhaus University Weimar（魏玛包豪斯大学）
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））
A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method
Technical University of Darmstadt（达姆施塔特工业大学）；RWTH Aachen University（亚琛工业大学）
A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials
Department of Mechanical and Production Engineering, Aarhus University（阿arhus大学机械与生产工程系）；Department of Applied Mathematics and Computer Science, Technical University of Denmark（技术大学 of Denmark应用数学与计算机科学系）
Pointwise Error Estimates for Numerical Physics-Informed Neural Networks
School of Computer Science, Georgia Institute of Technology（佐治亚理工学院计算机学院）；CentraleSupélec, Paris Saclay University（巴黎萨克雷大学中央理工-高等电力学院）；Transvalor SA（Transvalor公司）
Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；School of Computational Science and Engineering, Georgia Institute of Technology（佐治亚理工学院计算科学与工程学院）；Walker Department of Mechanical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校沃克机械工程系）
Radial Müntz-Szász Networks: Neural Architectures with Learnable Power Bases for Multidimensional Singularities
African Institute for Mathematical Sciences (AIMS), Research and Innovation Centre, Rwanda（非洲数学科学研究所（AIMS），研究与创新中心，卢旺达）；Graduate School of Engineering, The University of Tokyo, Japan（东京大学工学研究科，日本）；Axiom Research Group Department of Applied Mathematics and Computational Science, NM-AIST, Tanzania（Axiom研究组应用数学与计算科学系，NM-AIST，坦桑尼亚）
