Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity
Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295（波尔多大学、国家科学研究中心、波尔多INP、I2M、UMR 5295）；Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800（波尔多大学、国家科学研究中心、波尔多INP、LaBRI、UMR 5800）；Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295（艺术与技术学院技术学院、国家科学研究中心、波尔多INP、I2M、UMR 5295）
Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière, Michaël Clément
We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.
WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
School of Science, Harbin Institute of Technology, Shenzhen, P. R. China（哈尔滨工业大学深圳校区）；School of Science, Harbin Institute of Technology, Shenzhen, Guangdong（哈尔滨工业大学深圳校区）；Institute of Structural Mechanics, Bauhaus-Universität Weimar（魏玛 Bauhaus 大学结构力学研究所）
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院（KIT））；RWTH Aachen University（亚琛工业大学）
(Artificial) neural networks have become increasingly popular in mechanics to accelerate computations with model order reduction techniques and as universal models for a wide variety of materials. However, the major disadvantage of neural networks remains: their numerous parameters are challenging to interpret and explain. Thus, neural networks are often labeled as black boxes, and their results often elude human interpretation. In mechanics, the new and active field of physics-informed neural networks attempts to mitigate this disadvantage by designing deep neural networks on the basis of mec…
Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch
School of Artificial Intelligence, Anhui University（安徽大学人工智能学院）；School of Computer Science and Technology, Anhui University（安徽大学计算机科学与技术学院）；School of Physics and Electronic Information, Anhui Normal University（安徽师范大学物理与电子信息学院）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）
Physics-Informed Neural Networks for MIMO Beam Map and Environment Reconstruction
School of Science and Engineering（科学与工程学院）；Shenzhen Future Network of Intelligence Institute (FNii-Shenzhen)（深圳未来网络智能研究院）；Guangdong Provincial Key Laboratory of Future Networks of Intelligence（广东省未来网络智能重点实验室）
The introduction of Physics-informed Neural Networks (PINNs) has led to an increased interest in deep neural networks as universal approximators of PDEs in the solid mechanics community. Recently, the Deep Energy Method (DEM) has been proposed. DEM is based on energy minimization principles, contrary to PINN which is based on the residual of the PDEs. A significant advantage of DEM, is that it requires the approximation of lower order derivatives compared to formulations that are based on strong form residuals. However both DEM and classical PINN formulations struggle to resolve fine features …
National Center for Supercomputing Applications（国家超级计算应用中心）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening. The performance of this deep collocation method (DCM) depends on the architecture of the neural network and the corresponding hyperparameters. The presented DCM is meshfree and avoids any spatial discretization, which is usually needed for the finite element method (FEM). We …
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
Tsinghua University（清华大学）；Bauhaus-Universität Weimar（魏玛包豪斯大学）；CNPC Engineering Technology RD Company Limited（中国石油集团工程技术研究院有限公司）；Queensland University of Technology（昆士兰科技大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Defense Innovation Institute, Academy of Military Sciences（军事科学院国防科技创新研究院）
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation to reconstruct the temperature field from limited monitoring points, require large amounts of temperature tensors for an accurate estimation. This may decrease the availability and reliability of the system and sharply increase the monitoring cost. To solve this problem, this work develops a novel physics-informed deep reversible regression models …
Universidad de San Andrés（圣安德烈斯大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）
We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Benard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging …
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning models for high-fidelity data reconstruction require low-fidelity data for model training. Such requirement restrains the application performance of these models, since their data reconstruction accuracy would drop significantly if the low-fidelity input data used in model test has a large deviation from the training data. To overcome this restraint, we prop…
PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
Shahid Beheshti University（沙希德·贝赫什提大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所（IPM））；Cyberspace Research Institute, Shahid Beheshti University（沙希德·贝赫什提大学网络空间研究所）；University of Hertfordshire（赫特福德大学）
Technical University of Munich（慕尼黑工业大学）；University of Cambridge（剑桥大学）
We extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens …
Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time
Dynamics Group, Hamburg University of Technology, Germany（汉堡技术大学动力学组）；Department of Mechanical Engineering, Imperial College London, United Kingdom（伦敦帝国学院机械工程系）
Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
School of Advanced Manufacturing Engineering, Nanjing University（南京大学先进制造工程学院）；National Laboratory of Solid State Microstructures, Nanjing University（南京大学固态微结构国家实验室）；Suzhou Acoustics Industry Technology Research Institute Co., Ltd.（苏州声学工业技术研究所有限公司）；School of Mechanical and Electric Engineering, Soochow University（苏州大学机械与电子工程学院）；Shishan Laboratory, Nanjing University（仙山实验室）
College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航空航天学院）；Defense Innovation Institute, Chinese Academy of Military Science（中国人民解放军军事科学院国防创新研究院）
Temperature field reconstruction is essential for analyzing satellite heat reliability. As a representative machine learning model, the deep convolutional neural network (DCNN) is a powerful tool for reconstructing the satellite temperature field. However, DCNN needs a lot of labeled data to learn its parameters, which is contrary to the fact that actual satellite engineering can only acquire noisy unlabeled data. To solve the above problem, this paper proposes an unsupervised method, i.e., the physics-informed deep Monte Carlo quantile regression method, for reconstructing temperature field a…
Reconstructions of Jupiter's magnetic field using physics informed neural networks
School of Earth and Environment, University of Leeds（利兹大学地球与环境学院）；College of Science, Zhejiang University of Technology（浙江工业大学理学院）；College of Earth Sciences, Guilin University of Technology（桂林理工大学地球科学学院）；Leeds Institute for Data Analytics, University of Leeds（利兹大学利兹数据分析研究所）
Distributed physics-informed neural networks via domain decomposition for fast flow reconstruction
College of Control Science and Engineering（控制科学与工程学院）；School of Mathematical Sciences（数学科学学院）；Department of Mathematics（数学系）；State Key Laboratory of Industrial Control Technology（工业控制技术国家重点实验室）
Universidad de Valladolid（巴利亚多利德大学）；King’s College London（伦敦国王学院）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Centre for Marine Sciences - CCMAR（海洋科学中心（CCMAR））
First-pass perfusion cardiac magnetic resonance (FPP-CMR) is becoming an essential non-invasive imaging method for detecting deficits of myocardial blood flow, allowing the assessment of coronary heart disease. Nevertheless, acquisitions suffer from relatively low spatial resolution and limited heart coverage. Compressed sensing (CS) methods have been proposed to accelerate FPP-CMR and achieve higher spatial resolution. However, the long reconstruction times have limited the widespread clinical use of CS in FPP-CMR. Deep learning techniques based on supervised learning have emerged as alternat…
University of California at Santa Barbara（加州大学圣巴巴拉分校）；Massachusetts Institute of Technology（麻省理工学院）；New York University Grossman School of Medicine（纽约大学格罗斯曼医学院）
Electrical properties (EP), namely permittivity and electric conductivity, dictate the interactions between electromagnetic waves and biological tissue. EP can be potential biomarkers for pathology characterization, such as cancer, and improve therapeutic modalities, such radiofrequency hyperthermia and ablation. MR-based electrical properties tomography (MR-EPT) uses MR measurements to reconstruct the EP maps. Using the homogeneous Helmholtz equation, EP can be directly computed through calculations of second order spatial derivatives of the measured magnetic transmit or receive fields $(B_{1…
Physics-Informed Self-Supervised Learning for Joint Wire Calibration and Interaction Position Reconstruction in Multi-Wire Parallel Plate Avalanche Counters
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）；Technical University of Munich（慕尼黑工业大学）
We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN el…
College of Aerospace Science and Engineering National University of Defense Technology（国防科技大学航空航天学院）；Defense Innovation Institute Chinese Academy of Military Science（中国人民解放军军事科学院国防创新研究院）
For the temperature field reconstruction (TFR), a complex image-to-image regression problem, the convolutional neural network (CNN) is a powerful surrogate model due to the convolutional layer's good image feature extraction ability. However, a lot of labeled data is needed to train CNN, and the common CNN can not quantify the aleatoric uncertainty caused by data noise. In actual engineering, the noiseless and labeled training data is hardly obtained for the TFR. To solve these two problems, this paper proposes a deep Monte Carlo quantile regression (Deep MC-QR) method for reconstructing the t…
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）
3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks
Xinxiang Medical University（新乡医学院）；Institute of Particle and Nuclear Physics（粒子与核物理研究所）；Henan Normal University（河南师范大学）；Henan University of Urban Construction（河南城市学院）；Shanghai Institute of Applied Physics（上海应用物理研究所）；Chinese Academy of Sciences（中国科学院）；State Key Laboratory of Dark Matter Physics（暗物质物理国家重点实验室）；School of Physics and Astronomy（物理与天文学院）；Key Laboratory for Particle Astrophysics and Cosmology (Ministry of Education)（粒子天体物理与宇宙学重点实验室（教育部））；Shanghai Key Laboratory for Particle Physics and Cosmology（上海粒子物理与宇宙学重点实验室）；Scientific Model Research Group（科学模型研究组）
