Physics-informed machine learning

GE Karniadakis, IG Kevrekidis, L Lu… - Nature Reviews …, 2021‏ - nature.com
Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Reconstructing computational system dynamics from neural data with recurrent neural networks

D Durstewitz, G Koppe, MI Thurm - Nature Reviews Neuroscience, 2023‏ - nature.com
Computational models in neuroscience usually take the form of systems of differential
equations. The behaviour of such systems is the subject of dynamical systems theory …

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

H Gao, MJ Zahr, JX Wang - Computer Methods in Applied Mechanics and …, 2022‏ - Elsevier
Despite the great promise of the physics-informed neural networks (PINNs) in solving
forward and inverse problems, several technical challenges are present as roadblocks for …

PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs

P Ren, C Rao, Y Liu, JX Wang, H Sun - Computer Methods in Applied …, 2022‏ - Elsevier
Partial differential equations (PDEs) play a fundamental role in modeling and simulating
problems across a wide range of disciplines. Recent advances in deep learning have shown …

β-Variational autoencoders and transformers for reduced-order modelling of fluid flows

A Solera-Rico, C Sanmiguel Vila… - Nature …, 2024‏ - nature.com
Variational autoencoder architectures have the potential to develop reduced-order models
for chaotic fluid flows. We propose a method for learning compact and near-orthogonal …

Scalable transformer for pde surrogate modeling

Z Li, D Shu, A Barati Farimani - Advances in Neural …, 2023‏ - proceedings.neurips.cc
Transformer has shown state-of-the-art performance on various applications and has
recently emerged as a promising tool for surrogate modeling of partial differential equations …

[HTML][HTML] Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels

H Gao, L Sun, JX Wang - Physics of Fluids, 2021‏ - pubs.aip.org
High-resolution (HR) information of fluid flows, although preferable, is usually less
accessible due to limited computational or experimental resources. In many cases, fluid data …

Generative learning for forecasting the dynamics of high-dimensional complex systems

H Gao, S Kaltenbach, P Koumoutsakos - Nature Communications, 2024‏ - nature.com
We introduce generative models for accelerating simulations of high-dimensional systems
through learning and evolving their effective dynamics. In the proposed Generative Learning …

Predicting physics in mesh-reduced space with temporal attention

X Han, H Gao, T Pfaff, JX Wang, LP Liu - arxiv preprint arxiv:2201.09113, 2022‏ - arxiv.org
Graph-based next-step prediction models have recently been very successful in modeling
complex high-dimensional physical systems on irregular meshes. However, due to their …

Encoding physics to learn reaction–diffusion processes

C Rao, P Ren, Q Wang, O Buyukozturk… - Nature Machine …, 2023‏ - nature.com
Modelling complex spatiotemporal dynamical systems, such as reaction–diffusion
processes, which can be found in many fundamental dynamical effects in various …