A Finite Operator Learning Technique for Mapping the Elastic Properties of Microstructures to Their Mechanical Deformations DOI Creative Commons
Shahed Rezaei, Reza Najian Asl,

Shirko Faroughi

et al.

International Journal for Numerical Methods in Engineering, Journal Year: 2024, Volume and Issue: unknown

Published: Dec. 9, 2024

ABSTRACT To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of finite element with physics‐informed neural networks and concept operators. We propose directly utilizing available discretized weak form packages to construct loss functions algebraically, thereby demonstrating ability find even presence sharp discontinuities. Our focus is on micromechanics as an example, where knowledge deformation stress fields given heterogeneous microstructure crucial further design applications. The primary parameter under investigation Young's modulus distribution within system. investigations reveal physics‐based training yields higher accuracy compared purely data‐driven approaches unseen microstructures. Additionally, offer two methods improve process obtaining high‐resolution solutions, avoiding need use basic interpolation techniques. first one based autoencoder approach enhance efficiency calculation high resolution grid points. Next, Fourier‐based parametrization utilized address complex 2D 3D problems micromechanics. latter idea aims represent microstructures efficiently using Fourier coefficients. proposed draws from deep energy but generalizes enhances them by learning parametric without relying external data. Compared other operator frameworks, it leverages domain decomposition several ways: (1) uses shape derivatives instead automatic differentiation; (2) automatically includes node connectivity, making solver flexible approximating jumps solution fields; (3) can handle arbitrary shapes enforce boundary conditions. provided some initial comparisons well‐known algorithms, emphasize advantages newly method.

Language: Английский

A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics DOI
Chi Zhao, Feifei Zhang, Wenqiang Lou

et al.

Physics of Fluids, Journal Year: 2024, Volume and Issue: 36(10)

Published: Oct. 1, 2024

Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties field complex fluid dynamics. We thoroughly investigated design model architecture, optimization convergence rate, development modules for PINNs. However, efficiently accurately utilizing PINNs to resolve dynamics problems remain enormous barrier. For instance, rapidly deriving surrogate models turbulence from known characterizing flow details multiphase fields present substantial difficulties. Additionally, prediction parameters multi-physics coupled models, achieving balance across all scales multiscale modeling, developing standardized test sets encompassing dynamic are urgent technical breakthroughs needed. paper discusses latest advancements their potential applications dynamics, including turbulence, flows, multi-field flows. Furthermore, we analyze challenges face these outline future trends growth. Our objective is enhance integration deep learning facilitating resolution more realistic problems.

Language: Английский

Citations

17
Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media DOI Creative Commons
Salah A. Faroughi, Ramin Soltanmohammadi, Pingki Datta

et al.

Mathematics, Journal Year: 2023, Volume and Issue: 12(1), P. 63 - 63

Published: Dec. 24, 2023

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning accelerate simulation. We employ Physics-informed Neural Networks (PiNN) with periodic activation function solve problems both homogeneous and governed by advection-dispersion equation. Unlike neural networks that rely large training datasets, PiNNs use strong-form mathematical models constrain network phase simultaneously multiple dependent or independent field variables, such as pressure concentration fields. demonstrate effectiveness of using resolve media, we construct two functions, sin tanh, seven case studies, including 1D 2D scenarios. The accuracy PiNNs’ predictions is then evaluated absolute point error mean square metrics compared ground truth solutions obtained analytically numerically. Our results PiNN function, tanh up orders magnitude more accurate times faster train, especially media. Moreover, PiNN’s simultaneous fields can reduce expenses terms inference time three FEM simulations two-dimensional cases.

Language: Английский

Citations

30
The Application of Physics-Informed Machine Learning in Multiphysics Modeling in Chemical Engineering DOI
Zhi‐Yong Wu, Huan Wang, Chang He

et al.

Industrial & Engineering Chemistry Research, Journal Year: 2023, Volume and Issue: 62(44), P. 18178 - 18204

Published: Oct. 26, 2023

Physics-Informed Machine Learning (PIML) is an emerging computing paradigm that offers a new approach to tackle multiphysics modeling problems prevalent in the field of chemical engineering. These often involve complex transport processes, nonlinear reaction kinetics, and coupling. This Review provides detailed account main contributions PIML with specific emphasis on momentum transfer, heat mass reactions. The progress method development (e.g., algorithm architecture), software libraries, applications coupling surrogate modeling) are detailed. On this basis, future challenges highlight importance developing more practical solutions strategies for PIML, including turbulence models, domain decomposition, training acceleration, modeling, hybrid geometry module creation.

Language: Английский

Citations

25
Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems DOI
Antareep Kumar Sarma, Sumanta Roy, Chandrasekhar Annavarapu

et al.

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2024, Volume and Issue: 429, P. 117135 - 117135

Published: June 20, 2024

Language: Английский

Citations

15
Data-driven methods for flow and transport in porous media: A review DOI Creative Commons
Yang Guang, Ran Xu, Yusong Tian

et al.

International Journal of Heat and Mass Transfer, Journal Year: 2024, Volume and Issue: 235, P. 126149 - 126149

Published: Sept. 7, 2024

Language: Английский

Citations

10
Physics-informed radial basis function neural network for efficiently modeling oil–water two-phase Darcy flow DOI
Shuaijun Lv, Daolun Li, Wenshu Zha

et al.

Physics of Fluids, Journal Year: 2025, Volume and Issue: 37(1)

Published: Jan. 1, 2025

Physics-informed neural networks (PINNs) improve the accuracy and generalization ability of prediction by introducing physical constraints in training process. As a model combining laws deep learning, it has attracted wide attention. However, cost PINNs is high, especially for simulation more complex two-phase Darcy flow. In this study, physics-informed radial basis function network (PIRBFNN) proposed to simulate flow oil water efficiently. Specifically, each time step, phase equations are discretized based on finite volume method, then, loss constructed according residual their coupling equations, pressure approximated RBFNN. Based obtained pressure, another discrete equation saturation For boundary conditions, we use “hard constraints” speed up PIRBFNN. The straightforward structure PIRBFNN also contributes an efficient addition, have simply proved RBFNN fit continuous functions. Finally, experimental results verify computational efficiency Compared with convolutional network, reduced than three times.

Language: Английский

Citations

1
Effect and mechanism of the moisture content on the kinetic retardation of LNAPL pollutant migration by the capillary zone DOI
Kexue Han, Rui Zuo,

Ronggao Qin

et al.

Journal of Hazardous Materials, Journal Year: 2025, Volume and Issue: 487, P. 137266 - 137266

Published: Jan. 17, 2025

Language: Английский

Citations

1
Physics-informed neural network simulation of two-phase flow in heterogeneous and fractured porous media DOI
Xia Yan,

Jingqi Lin,

Sheng Wang

et al.

Advances in Water Resources, Journal Year: 2024, Volume and Issue: 189, P. 104731 - 104731

Published: May 23, 2024

Language: Английский

Citations

8
A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks DOI
François Lehmann, Marwan Fahs, Ali Alhubail

et al.

Advances in Water Resources, Journal Year: 2023, Volume and Issue: 181, P. 104564 - 104564

Published: Oct. 23, 2023

Language: Английский

Citations

15
Solving fluid flow in discontinuous heterogeneous porous media and multi-layer strata with interpretable physics-encoded finite element network DOI Creative Commons
Xi Wang, Wei Wu,

Hehua Zhu

et al.

Journal of Rock Mechanics and Geotechnical Engineering, Journal Year: 2024, Volume and Issue: unknown

Published: Dec. 1, 2024

Language: Английский

Citations

5