A Neural Solver for Variational Problems on CAD Geometries with Application to Electric Machine Simulation

11/17/2021
by   Moritz von Tresckow, et al.
0

This work presents a deep learning-based framework for the solution of partial differential equations on complex computational domains described with computer-aided design tools. To account for the underlying distribution of the training data caused by spline-based projections from the reference to the physical domain, a variational neural solver equipped with an importance sampling scheme is developed, such that the loss function based on the discretized energy functional obtained after the weak formulation is modified according to the sample distribution. To tackle multi-patch domains possibly leading to solution discontinuities, the variational neural solver is additionally combined with a domain decomposition approach based on the Discontinuous Galerkin formulation. The proposed neural solver is verified on a toy problem and then applied to a real-world engineering test case, namely that of electric machine simulation. The numerical results show clearly that the neural solver produces physics-conforming solutions of significantly improved accuracy.

READ FULL TEXT

page 16

page 17

page 18

research
09/24/2019

D3M: A deep domain decomposition method for partial differential equations

A state-of-the-art deep domain decomposition method (D3M) based on the v...
research
03/26/2021

Elvet – a neural network-based differential equation and variational problem solver

We present Elvet, a Python package for solving differential equations an...
research
12/21/2021

A Discontinuous Galerkin Solver in the FLASH Multi-Physics Framework

In this paper, we present a discontinuous Galerkin solver based on previ...
research
05/21/2023

ParticleWNN: a Novel Neural Networks Framework for Solving Partial Differential Equations

Deep neural networks (DNNs) have been widely used to solve partial diffe...
research
04/26/2021

Efficient training of physics-informed neural networks via importance sampling

Physics-Informed Neural Networks (PINNs) are a class of deep neural netw...
research
04/25/2020

Neural Network Solutions to Differential Equations in Non-Convex Domains: Solving the Electric Field in the Slit-Well Microfluidic Device

The neural network method of solving differential equations is used to a...
research
12/17/2021

A scalable DG solver for the electroneutral Nernst-Planck equations

The robust, scalable simulation of flowing electrochemical systems is in...

Please sign up or login with your details

Forgot password? Click here to reset