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2022

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.


Citation

@inproceedings witman2022neural title=Neural Basis Functions for Accelerating Solutions to high Mach Euler Equations author=David Witman and Alexander New and Hicham Alkandry and Honest Mrema booktitle=ICML 2022 2nd AI for Science Workshop year=2022 url=https://openreview.net/forum?id=dvqjD3peY5S

Citation

@inproceedings witman2022neural title=Neural Basis Functions for Accelerating Solutions to high Mach Euler Equations author=David Witman and Alexander New and Hicham Alkandry and Honest Mrema booktitle=ICML 2022 2nd AI for Science Workshop year=2022 url=https://openreview.net/forum?id=dvqjD3peY5S