A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

C Wu, M Zhu, Q Tan, Y Kartha, L Lu - Computer Methods in Applied …, 2023 - Elsevier
Physics-informed neural networks (PINNs) have shown to be effective tools for solving both
forward and inverse problems of partial differential equations (PDEs). PINNs embed the …

Deep learning in computational mechanics: a review

L Herrmann, S Kollmannsberger - Computational Mechanics, 2024 - Springer
The rapid growth of deep learning research, including within the field of computational
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …

Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior

S Subramanian, P Harrington… - Advances in …, 2024 - proceedings.neurips.cc
Pre-trained machine learning (ML) models have shown great performance for awide range
of applications, in particular in natural language processing (NLP) and computer vision (CV) …

Data-driven methods for flow and transport in porous media: a review

G Yang, R Xu, Y Tian, S Guo, J Wu, X Chu - International Journal of Heat …, 2024 - Elsevier
This review focuses on recent advancements in data-driven methods for analyzing flow and
transport in porous media, which are showing promising potential for applications in energy …

Enhancing PINNs for solving PDEs via adaptive collocation point movement and adaptive loss weighting

J Hou, Y Li, S Ying - Nonlinear Dynamics, 2023 - Springer
Physics-informed neural networks (PINNs) are an emerging method for solving partial
differential equations (PDEs) and have been widely applied in the field of scientific …

A physics-informed convolutional neural network for the simulation and prediction of two-phase Darcy flows in heterogeneous porous media

Z Zhang, X Yan, P Liu, K Zhang, R Han… - Journal of Computational …, 2023 - Elsevier
The physics-informed neural network (PINN) is a general deep learning framework for
simulating flows with limited or no labeled data. In the current study, we develop a physics …

Adaptive self-supervision algorithms for physics-informed neural networks

S Subramanian, RM Kirby, MW Mahoney… - ECAI 2023, 2023 - ebooks.iospress.nl
Physics-informed neural networks (PINNs) incorporate physical knowledge from the
problem domain as a soft constraint on the loss function, but recent work has shown that this …

VW-PINNs: A volume weighting method for PDE residuals in physics-informed neural networks

J Song, W Cao, F Liao, W Zhang - Acta Mechanica Sinica, 2025 - Springer
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving the
forward and inverse problems involving partial differential equations (PDEs). The method …

Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media

SA Faroughi, R Soltanmohammadi, P Datta… - Mathematics, 2023 - mdpi.com
Simulating solute transport in heterogeneous porous media poses computational
challenges due to the high-resolution meshing required for traditional solvers. To overcome …

Finite element-integrated neural network framework for elastic and elastoplastic solids

N Zhang, K Xu, ZY Yin, KQ Li, YF Jin - Computer Methods in Applied …, 2025 - Elsevier
The Physics-informed neural network method (PINN) has shown promise in resolving
unknown physical fields in solid mechanics, owing to its success in solving various partial …