Partial differential equations for training deep neural networks

This paper establishes a connection between non-convex optimization and nonlinear partial differential equations (PDEs). We interpret empirically successful ...

Partial Differential Equations Meet Deep Neural Networks: A Survey

Recently, another equally important paradigm, data-based computation represented by deep learning, has emerged as an effective means of solving ...

partial differential equations for optimizing deep neural networks

Abstract:In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear ...

PARTIAL DIFFERENTIAL EQUATIONS FOR OPTIMIZING DEEP ...

Abstract: In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial ...

A neural network-based PDE solving algorithm with high precision

An innovative method is introduced in this study to solve linear equations based on deep neural networks. To achieve a high accuracy, we employ the residual ...

Solving high-dimensional partial differential equations using deep ...

To this end, the PDEs are reformulated using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural ...

Deep Learning for Partial Differential Equations (PDEs)

Figure 1: Data Generation for Training the Neural Network. We sample randomly from the inner domain and its boundary on. Here x represents the sampling points ...

Deep neural networks and partial differential equations

They excel in training complex models on a large amount of data, while being computationally effective at inference. However, for physical ...

Solving Partial Differential Equations With Neural Networks - uu .diva

Physics-. Informed Neural Networks and the Deep Ritz Method are unsupervised ma- chine learning methods, while the Fourier Neural Operator is a supervised.

Transfer learning for deep neural network-based partial differential ...

Deep neural networks (DNNs) have recently shown great potential in solving partial differential equations (PDEs). The success of neural ...

Latest Neural Nets Solve World's Hardest Equations Faster Than ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model ...

Multi-level physics informed deep learning for solving partial ...

Physics-informed neural network has emerged as a promising approach for solving partial differential equations.

r-Adaptive deep learning method for solving partial differential ...

We introduce a Deep Neural Network (DNN) method for solving Partial Differential Equations (PDEs) that simultaneously: (a) constructs an optimal r-adapted mesh.

Train a Deep Neural Network by Minimizing an Energy Function to ...

The numerical solution of partial differential equations (PDEs) is a crucial component of scientific computing. The idea of using a neural ...

Deep learning methods for partial differential equations and related ...

Specifically, more and more neural network (NN) architectures have been developed to solve specific classes of partial differential equations (PDEs). Such ...

Solving differential equations using deep neural networks

Recent work on solving partial differential equations (PDEs) with deep neural networks (DNNs) is presented. The paper reviews and extends ...

Solving Partial Differential Equations Using Deep Learning and ...

Because an artificial neural network can be used as a function approximator, it can be considered as a learnable function and applied to solve partial ...

Three ways to solve partial differential equations with neural ...

PDE solvers based on (deep) neural networks typically cannot compete with classical numerical solution methods in low to moderate dimensions—in ...

partial differential equations for optimizing deep neural networks

The modified, or relaxed, loss function is the solution of a viscous Hamilton–Jacobi partial differential equation (PDE). Experimental results ...

Deep Learning and Computations of PDEs by Siddhartha Mishra

COLLOQUIUM DEEP LEARNING AND COMPUTATIONS OF PDES SPEAKER: Siddhartha Mishra (Professor of Applied Mathematics, ETH Zürich, ...