Operator Compression with Deep Neural Networks

05/25/2021
by   Fabian Kröpfl, et al.
0

This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales. Based on existing methods that compress such a multiscale operator to a finite-dimensional sparse surrogate model on a given target scale, we propose to directly approximate the coefficient-to-surrogate map with a neural network. We emulate local assembly structures of the surrogates and thus only require a moderately sized network that can be trained efficiently in an offline phase. This enables large compression ratios and the online computation of a surrogate based on simple forward passes through the network is substantially accelerated compared to classical numerical upscaling approaches. We apply the abstract framework to a family of prototypical second-order elliptic heterogeneous diffusion operators as a demonstrating example.

READ FULL TEXT

page 17

page 18

page 19

research
11/03/2021

A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks

Neural networks are powerful tools for approximating high dimensional da...
research
12/15/2021

Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations

We construct deep operator networks (ONets) between infinite-dimensional...
research
01/17/2023

Operator Learning Framework for Digital Twin and Complex Engineering Systems

With modern computational advancements and statistical analysis methods,...
research
02/04/2023

A neural operator-based surrogate solver for free-form electromagnetic inverse design

Neural operators have emerged as a powerful tool for solving partial dif...
research
02/02/2018

Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification

State-of-the-art computer codes for simulating real physical systems are...
research
02/23/2023

Learning stiff chemical kinetics using extended deep neural operators

We utilize neural operators to learn the solution propagator for the cha...
research
02/07/2023

Learning bias corrections for climate models using deep neural operators

Numerical simulation for climate modeling resolving all important scales...

Please sign up or login with your details

Forgot password? Click here to reset