Scientific machine learning through physics–informed neural networks: Where we are and what's next

S Cuomo, VS Di Cola, F Giampaolo, G Rozza… - Journal of Scientific …, 2022 - Springer
Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

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 …

Characterizing possible failure modes in physics-informed neural networks

A Krishnapriyan, A Gholami, S Zhe… - Advances in neural …, 2021 - proceedings.neurips.cc
Recent work in scientific machine learning has developed so-called physics-informed neural
network (PINN) models. The typical approach is to incorporate physical domain knowledge …

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

J Yu, L Lu, X Meng, GE Karniadakis - Computer Methods in Applied …, 2022 - Elsevier
Deep learning has been shown to be an effective tool in solving partial differential equations
(PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual …

Combustion machine learning: Principles, progress and prospects

M Ihme, WT Chung, AA Mishra - Progress in Energy and Combustion …, 2022 - Elsevier
Progress in combustion science and engineering has led to the generation of large amounts
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …

Interpretable machine learning: Fundamental principles and 10 grand challenges

C Rudin, C Chen, Z Chen, H Huang… - Statistic …, 2022 - projecteuclid.org
Interpretability in machine learning (ML) is crucial for high stakes decisions and
troubleshooting. In this work, we provide fundamental principles for interpretable ML, and …

Respecting causality is all you need for training physics-informed neural networks

S Wang, S Sankaran, P Perdikaris - arxiv preprint arxiv:2203.07404, 2022 - arxiv.org
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this
date PINNs have not been successful in simulating dynamical systems whose solution …

On neural differential equations

P Kidger - arxiv preprint arxiv:2202.02435, 2022 - arxiv.org
The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Physics-informed neural networks for heat transfer problems

S Cai, Z Wang, S Wang… - Journal of Heat …, 2021 - asmedigitalcollection.asme.org
Physics-informed neural networks (PINNs) have gained popularity across different
engineering fields due to their effectiveness in solving realistic problems with noisy data and …

A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

E Haghighat, M Raissi, A Moure, H Gomez… - Computer Methods in …, 2021 - Elsevier
We present the application of a class of deep learning, known as Physics Informed Neural
Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how …