Integrating scientific knowledge with machine learning for engineering and environmental systems
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …
require novel methodologies that are able to integrate traditional physics-based modeling …
An overview on deep learning-based approximation methods for partial differential equations
It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
[PDF][PDF] Integrating physics-based modeling with machine learning: A survey
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …
require novel methodologies that are able to integrate traditional physics-based modeling …
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
We formulate a general framework for hp-variational physics-informed neural networks (hp-
VPINNs) based on the nonlinear approximation of shallow and deep neural networks and …
VPINNs) based on the nonlinear approximation of shallow and deep neural networks and …
Weak adversarial networks for high-dimensional partial differential equations
Solving general high-dimensional partial differential equations (PDE) is a long-standing
challenge in numerical mathematics. In this paper, we propose a novel approach to solve …
challenge in numerical mathematics. In this paper, we propose a novel approach to solve …
Solving parametric PDE problems with artificial neural networks
The curse of dimensionality is commonly encountered in numerical partial differential
equations (PDE), especially when uncertainties have to be modelled into the equations as …
equations (PDE), especially when uncertainties have to be modelled into the equations as …
Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
In recent years, deep learning has proven to be a viable methodology for surrogate
modeling and uncertainty quantification for a vast number of physical systems. However, in …
modeling and uncertainty quantification for a vast number of physical systems. However, in …
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …
partial differential equations (PDEs) in a very high dimension, using ideas from either …
A high-efficient hybrid physics-informed neural networks based on convolutional neural network
Z Fang - IEEE Transactions on Neural Networks and Learning …, 2021 - ieeexplore.ieee.org
In this article, we develop a hybrid physics-informed neural network (hybrid PINN) for partial
differential equations (PDEs). We borrow the idea from the convolutional neural network …
differential equations (PDEs). We borrow the idea from the convolutional neural network …
Neural jump stochastic differential equations
Many time series are effectively generated by a combination of deterministic continuous
flows along with discrete jumps sparked by stochastic events. However, we usually do not …
flows along with discrete jumps sparked by stochastic events. However, we usually do not …