Scientific machine learning through physics–informed neural networks: Where we are and what's next
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 …
model equations, like Partial Differential Equations (PDE), as a component of the neural …
Physics-informed machine learning
Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …
Characterizing possible failure modes in physics-informed neural networks
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 …
network (PINN) models. The typical approach is to incorporate physical domain knowledge …
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
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 …
(PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual …
Combustion machine learning: Principles, progress and prospects
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 …
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …
Interpretable machine learning: Fundamental principles and 10 grand challenges
Interpretability in machine learning (ML) is crucial for high stakes decisions and
troubleshooting. In this work, we provide fundamental principles for interpretable ML, 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
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 …
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 …
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …
Physics-informed neural networks for heat transfer problems
Physics-informed neural networks (PINNs) have gained popularity across different
engineering fields due to their effectiveness in solving realistic problems with noisy data and …
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
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 …
Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how …