An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications

27 August 2019

E. Samaniego

C. Anitescu

S. Goswami

Vien Minh Nguyen-Thanh

Timon Rabczuk

Papers citing "An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications"

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Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation Yizheng Wang Jinshuai Bai M. Eshaghi C. Anitescu X. Zhuang Timon Rabczuk Yinghua Liu AI4CE 59 1 0 02 Feb 2025
Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG Signals Shuhao Ma Jie Zhang Chaoyang Shi Pei Di Ian D. Robertson Zhi-Qiang Zhang 84 8 0 05 Dec 2024
On the Boundary Feasibility for PDE Control with Neural Operators Hanjiang Hu Changliu Liu AI4CE 72 1 0 23 Nov 2024
A Variational Bayesian Inference Theory of Elasticity and Its Mixed Probabilistic Finite Element Method for Inverse Deformation Solutions in Any Dimension Chao Wang Shaofan Li 16 0 0 10 Oct 2024
Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems M. Chenaud Frédéric Magoulès José Alves AI4CE PINN 28 1 0 25 Sep 2024
Harnessing physics-informed operators for high-dimensional reliability analysis problems N Navaneeth Tushar Souvik Chakraborty AI4CE 38 0 0 07 Sep 2024
Physics-informed DeepONet with stiffness-based loss functions for structural response prediction Bilal Ahmed Yuqing Qiu Diab W. Abueidda Waleed El-Sekelly Borja Garcia de Soto Tarek Abdoun M. Mobasher 18 0 0 02 Sep 2024
Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid Subhankar Sarkar Souvik Chakraborty 25 0 0 01 Sep 2024
Physics Informed Deep Learning for Strain Gradient Continuum Plasticity Ankit Tyagi Uttam Suman Mariya Mamajiwala Debasish Roy PINN AI4CE 19 1 0 13 Aug 2024
DeepNetBeam: A Framework for the Analysis of Functionally Graded Porous Beams M. Eshaghi M. Bamdad C. Anitescu Yizheng Wang X. Zhuang Timon Rabczuk AI4CE 29 7 0 04 Aug 2024
Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity Honghui Du Binyao Guo QiZhi He AI4CE 38 0 0 15 Jul 2024
Physics and geometry informed neural operator network with application to acoustic scattering S. Nair Timothy F. Walsh Greg Pickrell Fabio Semperlotti AI4CE 36 2 0 02 Jun 2024
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A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains Yusuke Yamazaki Ali Harandi Mayu Muramatsu A. Viardin Markus Apel T. Brepols Stefanie Reese Shahed Rezaei AI4CE 36 12 0 21 May 2024
Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materials Thi Nguyen Khoa Nguyen T. Dairay Raphael Meunier Christophe Millet Mathilde Mougeot AI4CE PINN 33 0 0 06 May 2024
Derivative-based regularization for regression Enrico Lopedoto Maksim Shekhunov Vitaly Aksenov K. Salako Tillman Weyde 23 0 0 01 May 2024
A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations Shahed Rezaei Reza Najian Asl S. Faroughi Mahdi Asgharzadeh Ali Harandi Rasoul Najafi Koopas G. Laschet Stefanie Reese Markus Apel AI4CE 39 4 0 28 Mar 2024
Separable Physics-Informed Neural Networks for the solution of elasticity problems V. A. Es'kin Danil V. Davydov Julia V. Guréva Alexey O. Malkhanov Mikhail E. Smorkalov PINN AI4CE 20 2 0 24 Jan 2024
N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for Boundary Value Problems Jonghyuk Baek Yanran Wang J. S. Chen 27 1 0 16 Jan 2024
Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations Shahed Rezaei Ahmad Moeineddin Michael Kaliske Markus Apel AI4CE 38 5 0 04 Jan 2024
Dynamically configured physics-informed neural network in topology optimization applications Ji-Cheng Yin Ziming Wen Shuhao Li Yaya Zhang Hu Wang AI4CE PINN 38 4 0 12 Dec 2023
Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics Honghui Du QiZhi He AI4CE 52 4 0 21 Nov 2023
TSONN: Time-stepping-oriented neural network for solving partial differential equations W. Cao Weiwei Zhang AI4TS 11 1 0 25 Oct 2023
Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks T. Şahin M. Danwitz A. Popp PINN 31 19 0 24 Aug 2023
Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables Javier Orera-Echeverria J. Ayensa-Jiménez Manuel Doblaré 25 1 0 07 Aug 2023
A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture Jonghyuk Baek Jiun-Shyan Chen 18 12 0 04 Jul 2023
Data driven localized wave solution of the Fokas-Lenells equation using modified PINN G. K. Saharia Sagardeep Talukdar Riki Dutta S. Nandy 11 1 0 03 Jun 2023
DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks Aditya Joglekar Hongrui Chen L. Kara AI4CE 18 12 0 06 May 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 35 5 0 26 Apr 2023
Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs Jinshuai Bai Guirong Liu Ashish Gupta Laith Alzubaidi Xinzhu Feng Yuantong T. Gu PINN 16 1 0 13 Apr 2023
Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN Shahed Rezaei Ahmad Moeineddin Ali Harandi PINN 32 18 0 10 Apr 2023
Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations Tengfei Xu Dachuan Liu Peng Hao Bo Wang 36 4 0 09 Apr 2023
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks K. Michałowska S. Goswami George Karniadakis S. Riemer-Sørensen AI4CE 15 15 0 03 Mar 2023
Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook Xuan Di Rongye Shi Zhaobin Mo Yongjie Fu PINN AI4TS AI4CE 24 28 0 03 Mar 2023
Physics-aware deep learning framework for linear elasticity Anisha Roy Rikhi Bose AI4CE 35 8 0 19 Feb 2023
Physics informed WNO N. N. Tapas Tripura S. Chakraborty 25 28 0 12 Feb 2023
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation Rui Zhang Qi Meng Rongchan Zhu Yue Wang Wenlei Shi Shihua Zhang Zhi-Ming Ma Tie-Yan Liu DiffM AI4CE 51 4 0 10 Feb 2023
Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains Ali Harandi Ahmad Moeineddin Michael Kaliske Stefanie Reese Shahed Rezaei AI4CE PINN 22 42 0 09 Feb 2023
BINN: A deep learning approach for computational mechanics problems based on boundary integral equations Jia Sun Yinghua Liu Yizheng Wang Z. Yao Xiao-ping Zheng PINN AI4CE 22 23 0 11 Jan 2023
Lab-scale Vibration Analysis Dataset and Baseline Methods for Machinery Fault Diagnosis with Machine Learning Bagus Tris Atmaja Haris Ihsannur Suyanto D. Arifianto 11 11 0 27 Dec 2022
Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems Tapas Tripura A. Desai S. Adhikari S. Chakraborty AI4CE 30 23 0 19 Dec 2022
Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data D. Anton Henning Wessels AI4CE 28 7 0 15 Dec 2022
Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics Saurabh Deshpande Raúl I. Sosa Stéphane P. A. Bordas J. Lengiewicz AI4CE 30 18 0 01 Dec 2022
Utilising physics-guided deep learning to overcome data scarcity Jinshuai Bai Laith Alzubaidi Qingxia Wang E. Kuhl Bennamoun Yuantong T. Gu PINN AI4CE 26 3 0 24 Nov 2022
Neural PDE Solvers for Irregular Domains Biswajit Khara Ethan Herron Zhanhong Jiang Aditya Balu Chih-Hsuan Yang ... Anushrut Jignasu S. Sarkar C. Hegde A. Krishnamurthy Baskar Ganapathysubramanian AI4CE 22 7 0 07 Nov 2022
MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations Saurabh Deshpande Stéphane P. A. Bordas J. Lengiewicz AI4CE GNN 82 28 0 01 Nov 2022
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 24 17 0 27 Oct 2022