Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations
Abstract
We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where we regress a set of neural networks onto a reduced order Proper Orthogonal Decomposition (POD) basis. These networks are then used in combination with a branch network that ingests the parameters of the prescribed PDE to compute a reduced order approximation to the PDE. This approach is applied to the steady state Euler equations for high speed flow conditions (mach 10-30) where we consider the 2D flow around a cylinder which develops a shock condition. We then use the NBF predictions as initial conditions to a high fidelity Computational Fluid Dynamics (CFD) solver (CFD++) to show faster convergence. Lessons learned for training and implementing this algorithm will be presented as well.
Cite
@article{arxiv.2208.01687,
title = {Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations},
author = {David Witman and Alexander New and Hicham Alkendry and Honest Mrema},
journal= {arXiv preprint arXiv:2208.01687},
year = {2022}
}
Comments
Published at ICML 2022 AI for Science workshop: https://openreview.net/forum?id=dvqjD3peY5S