An overview on deep learning-based approximation methods for partial differential equations
C Beck, M Hutzenthaler, A Jentzen… - ar**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …
modeling of complex dynamic processes across all corners of science and engineering …
Fourier neural operator for parametric partial differential equations
Z Li, N Kovachki, K Azizzadenesheli, B Liu… - ar**s
between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural …
between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural …
Multiwavelet-based operator learning for differential equations
The solution of a partial differential equation can be obtained by computing the inverse
operator map between the input and the solution space. Towards this end, we introduce a …
operator map between the input and the solution space. Towards this end, we introduce a …
DeepXDE: A deep learning library for solving differential equations
Deep learning has achieved remarkable success in diverse applications; however, its use in
solving partial differential equations (PDEs) has emerged only recently. Here, we present an …
solving partial differential equations (PDEs) has emerged only recently. Here, we present an …
A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
A physics informed neural network (PINN) incorporates the physics of a system by satisfying
its boundary value problem through a neural network's loss function. The PINN approach …
its boundary value problem through a neural network's loss function. The PINN approach …
Model reduction and neural networks for parametric PDEs
We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …
between infinitedimensional spaces. The proposed approach is motivated by the recent …
Frequency principle: Fourier analysis sheds light on deep neural networks
We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis
perspective. We demonstrate a very universal Frequency Principle (F-Principle)---DNNs …
perspective. We demonstrate a very universal Frequency Principle (F-Principle)---DNNs …
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of
numerically solving partial differential equations (PDEs) without the need of building …
numerically solving partial differential equations (PDEs) without the need of building …