1. Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations
- Author
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Witman, David, New, Alexander, Alkendry, Hicham, and Mrema, Honest
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,FOS: Mathematics ,Mathematics - Numerical Analysis ,Numerical Analysis (math.NA) ,Statistics - Computation ,Computation (stat.CO) ,Machine Learning (cs.LG) - 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., Comment: Published at ICML 2022 AI for Science workshop: https://openreview.net/forum?id=dvqjD3peY5S
- Published
- 2022
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