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An Energy Approach to the Solution of Partial Differential Equations in
  Computational Mechanics via Machine Learning: Concepts, Implementation and
  Applications
v1v2 (latest)

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

Computer Methods in Applied Mechanics and Engineering (CMAME), 2019
27 August 2019
E. Samaniego
C. Anitescu
S. Goswami
Vien Minh Nguyen-Thanh
Hongwei Guo
Khader M. Hamdia
Timon Rabczuk
X. Zhuang
    PINNAI4CE
ArXiv (abs)PDFHTML

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

50 / 106 papers shown
Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains
Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains
M. V. Tresckow
Ion Gabriel Ion
Dimitrios Loukrezis
AI4CE
167
0
0
29 Sep 2025
Understanding the Capabilities of Molecular Graph Neural Networks in Materials Science Through Multimodal Learning and Physical Context Encoding
Understanding the Capabilities of Molecular Graph Neural Networks in Materials Science Through Multimodal Learning and Physical Context Encoding
Can Polat
Hasan Kurban
Erchin Serpedin
Mustafa Kurban
AI4CE
324
1
0
17 May 2025
Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures
Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structuresEngineering applications of artificial intelligence (EAAI), 2025
Bilal Ahmed
Yuqing Qiu
Diab W. Abueidda
Waleed El-Sekelly
Tarek Abdoun
M. Mobasher
AI4CE
242
1
0
11 May 2025
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEsComputer Methods in Applied Mechanics and Engineering (CMAME), 2025
Sidharth S. Menon
Ameya D. Jagtap
PINN
934
10
0
06 May 2025
Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning
Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning
Shota Deguchi
Mitsuteru Asai
PINNAI4CE
654
0
0
25 Apr 2025
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
Hamidreza Eivazi
Jendrik-Alexander Tröger
Stefan H. A. Wittek
Stefan Hartmann
Andreas Rausch
AI4CE
538
2
0
27 Mar 2025
Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation
Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank AdaptationInternational Journal of Mechanical System Dynamics (IJMSD), 2025
Yizheng Wang
Jinshuai Bai
M. Eshaghi
C. Anitescu
X. Zhuang
Timon Rabczuk
Yinghua Liu
AI4CE
480
34
0
02 Feb 2025
Physics-informed Deep Learning for Muscle Force Prediction with
  Unlabeled sEMG Signals
Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG SignalsIEEE transactions on neural systems and rehabilitation engineering (IEEE TNSRE), 2024
Shuhao Ma
Jie Zhang
Chaoyang Shi
Pei Di
Ian D. Robertson
Zhi-Qiang Zhang
324
22
0
05 Dec 2024
A Variational Bayesian Inference Theory of Elasticity and Its Mixed
  Probabilistic Finite Element Method for Inverse Deformation Solutions in Any
  Dimension
A Variational Bayesian Inference Theory of Elasticity and Its Mixed Probabilistic Finite Element Method for Inverse Deformation Solutions in Any DimensionIEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2024
Chao Wang
Shaofan Li
173
2
0
10 Oct 2024
Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for
  complex problems
Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problemsAdvances in Engineering Software (Adv. Eng. Softw.), 2024
M. Chenaud
Frédéric Magoulès
José Alves
AI4CEPINN
224
3
0
25 Sep 2024
Physics aware machine learning for micromagnetic energy minimization:
  recent algorithmic developments
Physics aware machine learning for micromagnetic energy minimization: recent algorithmic developmentsComputer Physics Communications (CPC), 2024
Sebastian Schaffer
T. Schrefl
Harald Oezelt
Norbert J Mauser
Lukas Exl
AI4CE
280
0
0
19 Sep 2024
Harnessing physics-informed operators for high-dimensional reliability
  analysis problems
Harnessing physics-informed operators for high-dimensional reliability analysis problemsProbabilistic Engineering Mechanics (PEM), 2024
N Navaneeth
Tushar
Souvik Chakraborty
AI4CE
199
2
0
07 Sep 2024
Physics-informed DeepONet with stiffness-based loss functions for
  structural response prediction
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
241
2
0
02 Sep 2024
Spatio-spectral graph neural operator for solving computational
  mechanics problems on irregular domain and unstructured grid
Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured gridComputer Methods in Applied Mechanics and Engineering (CMAME), 2024
Subhankar Sarkar
Souvik Chakraborty
210
7
0
01 Sep 2024
Physics Informed Deep Learning for Strain Gradient Continuum Plasticity
Physics Informed Deep Learning for Strain Gradient Continuum Plasticity
Ankit Tyagi
Uttam Suman
Mariya Mamajiwala
Debasish Roy
PINNAI4CE
260
1
0
13 Aug 2024
DeepNetBeam: A Framework for the Analysis of Functionally Graded Porous
  Beams
DeepNetBeam: A Framework for the Analysis of Functionally Graded Porous Beams
M. Eshaghi
M. Bamdad
C. Anitescu
Yizheng Wang
X. Zhuang
Timon Rabczuk
AI4CE
283
25
0
04 Aug 2024
Differentiable Neural-Integrated Meshfree Method for Forward and Inverse
  Modeling of Finite Strain Hyperelasticity
Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity
Honghui Du
Binyao Guo
QiZhi He
AI4CE
248
6
0
15 Jul 2024
Physics and geometry informed neural operator network with application
  to acoustic scattering
Physics and geometry informed neural operator network with application to acoustic scattering
S. Nair
Timothy F. Walsh
Greg Pickrell
Fabio Semperlotti
AI4CE
229
5
0
02 Jun 2024
Physics informed cell representations for variational formulation of
  multiscale problems
Physics informed cell representations for variational formulation of multiscale problems
Yuxiang Gao
Soheil Kolouri
R. Duddu
AI4CE
241
1
0
27 May 2024
A finite element-based physics-informed operator learning framework for
  spatiotemporal partial differential equations on arbitrary domains
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
418
32
0
21 May 2024
Geometry-aware framework for deep energy method: an application to
  structural mechanics with hyperelastic materials
Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materialsComputer Physics Communications (CPC), 2024
Thi Nguyen Khoa Nguyen
T. Dairay
Raphael Meunier
Christophe Millet
Mathilde Mougeot
AI4CEPINN
248
4
0
06 May 2024
Derivative-based regularization for regression
Derivative-based regularization for regression
Enrico Lopedoto
Maksim Shekhunov
Vitaly Aksenov
K. Salako
Tillman Weyde
264
0
0
01 May 2024
A finite operator learning technique for mapping the elastic properties
  of microstructures to their mechanical deformations
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
425
17
0
28 Mar 2024
Separable Physics-Informed Neural Networks for the solution of
  elasticity problems
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
PINNAI4CE
365
6
0
24 Jan 2024
N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for
  Boundary Value Problems
N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for Boundary Value ProblemsComputer Methods in Applied Mechanics and Engineering (CMAME), 2024
Jonghyuk Baek
Yanran Wang
J. S. Chen
288
3
0
16 Jan 2024
Integration of physics-informed operator learning and finite element
  method for parametric learning of partial differential equations
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
354
5
0
04 Jan 2024
Dynamically configured physics-informed neural network in topology
  optimization applications
Dynamically configured physics-informed neural network in topology optimization applications
Ji-Cheng Yin
Ziming Wen
Shuhao Li
Yaya Zhang
Hu Wang
AI4CEPINN
254
9
0
12 Dec 2023
Neural-Integrated Meshfree (NIM) Method: A differentiable
  programming-based hybrid solver for computational mechanics
Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanicsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Honghui Du
QiZhi He
AI4CE
474
15
0
21 Nov 2023
TSONN: Time-stepping-oriented neural network for solving partial
  differential equations
TSONN: Time-stepping-oriented neural network for solving partial differential equations
W. Cao
Weiwei Zhang
AI4TS
214
3
0
25 Oct 2023
Solving Forward and Inverse Problems of Contact Mechanics using
  Physics-Informed Neural Networks
Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural NetworksAdvanced Modeling and Simulation in Engineering Sciences (AMSES), 2023
T. Şahin
M. Danwitz
A. Popp
PINN
261
55
0
24 Aug 2023
Predicting and explaining nonlinear material response using deep
  Physically Guided Neural Networks with Internal Variables
Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal VariablesMathematics and mechanics of solids (MMS), 2023
Javier Orera-Echeverria
J. Ayensa-Jiménez
Manuel Doblaré
354
3
0
07 Aug 2023
A Neural Network-Based Enrichment of Reproducing Kernel Approximation
  for Modeling Brittle Fracture
A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle FractureComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Jonghyuk Baek
Jiun-Shyan Chen
237
21
0
04 Jul 2023
Data driven localized wave solution of the Fokas-Lenells equation using
  modified PINN
Data driven localized wave solution of the Fokas-Lenells equation using modified PINN
G. K. Saharia
Sagardeep Talukdar
Riki Dutta
S. Nandy
129
1
0
03 Jun 2023
DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks
DMF-TONN: Direct Mesh-free Topology Optimization using Neural NetworksEngineering computations (Eng. Comput.), 2023
Aditya Joglekar
Hongrui Chen
Levent Burak Kara
AI4CE
199
22
0
06 May 2023
A Survey on Solving and Discovering Differential Equations Using Deep
  Neural Networks
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
322
7
0
26 Apr 2023
Physics-informed radial basis network (PIRBN): A local approximating
  neural network for solving nonlinear PDEs
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
272
1
0
13 Apr 2023
Learning solution of nonlinear constitutive material models using
  physics-informed neural networks: COMM-PINN
Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINNComputational Mechanics (CM), 2023
Shahed Rezaei
Ahmad Moeineddin
Ali Harandi
PINN
251
41
0
10 Apr 2023
Variational operator learning: A unified paradigm marrying training
  neural operators and solving partial differential equations
Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equationsJournal of the mechanics and physics of solids (JMPS), 2023
Tengfei Xu
Dachuan Liu
Peng Hao
Bo Wang
411
12
0
09 Apr 2023
Neural Operator Learning for Long-Time Integration in Dynamical Systems
  with Recurrent Neural Networks
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural NetworksIEEE International Joint Conference on Neural Network (IJCNN), 2023
K. Michałowska
S. Goswami
George Karniadakis
S. Riemer-Sørensen
AI4CE
337
36
0
03 Mar 2023
Physics-Informed Deep Learning For Traffic State Estimation: A Survey
  and the Outlook
Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook
Xuan Di
Rongye Shi
Chengbo Zang
Yongjie Fu
PINNAI4TSAI4CE
313
50
0
03 Mar 2023
Physics-aware deep learning framework for linear elasticity
Physics-aware deep learning framework for linear elasticity
Anisha Roy
Rikhi Bose
AI4CE
361
9
0
19 Feb 2023
Physics informed WNO
Physics informed WNOComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
N. N.
Tapas Tripura
S. Chakraborty
238
45
0
12 Feb 2023
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic RepresentationIEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2023
Rui Zhang
Qi Meng
Rongchan Zhu
Yue Wang
Wenlei Shi
Shihua Zhang
Zhi-Ming Ma
Tie-Yan Liu
DiffMAI4CE
930
14
0
10 Feb 2023
Mixed formulation of physics-informed neural networks for
  thermo-mechanically coupled systems and heterogeneous domains
Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainsInternational Journal for Numerical Methods in Engineering (IJNME), 2023
Ali Harandi
Ahmad Moeineddin
Michael Kaliske
Stefanie Reese
Shahed Rezaei
AI4CEPINN
320
71
0
09 Feb 2023
Randomized prior wavelet neural operator for uncertainty quantification
Randomized prior wavelet neural operator for uncertainty quantificationProbabilistic Engineering Mechanics (PEM), 2023
Shailesh Garg
S. Chakraborty
UQCVBDL
248
2
0
02 Feb 2023
BINN: A deep learning approach for computational mechanics problems
  based on boundary integral equations
BINN: A deep learning approach for computational mechanics problems based on boundary integral equationsComputer Methods in Applied Mechanics and Engineering (CMAME), 2023
Jia Sun
Yinghua Liu
Yizheng Wang
Z. Yao
Xiao-ping Zheng
PINNAI4CE
159
52
0
11 Jan 2023
Lab-scale Vibration Analysis Dataset and Baseline Methods for Machinery
  Fault Diagnosis with Machine Learning
Lab-scale Vibration Analysis Dataset and Baseline Methods for Machinery Fault Diagnosis with Machine Learning
Bagus Tris Atmaja
Haris Ihsannur
Suyanto
D. Arifianto
159
23
0
27 Dec 2022
Probabilistic machine learning based predictive and interpretable
  digital twin for dynamical systems
Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems
Tapas Tripura
A. Desai
S. Adhikari
S. Chakraborty
AI4CE
178
32
0
19 Dec 2022
Physics-Informed Neural Networks for Material Model Calibration from
  Full-Field Displacement Data
Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data
D. Anton
Henning Wessels
AI4CE
321
10
0
15 Dec 2022
Convolution, aggregation and attention based deep neural networks for
  accelerating simulations in mechanics
Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanicsFrontiers in Materials (Front. Mater.), 2022
Saurabh Deshpande
Raúl I. Sosa
Stéphane P. A. Bordas
J. Lengiewicz
AI4CE
305
25
0
01 Dec 2022
123
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