Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations

• URL: http://arxiv.org/abs/2208.01687v1
• Date: Tue, 2 Aug 2022 18:27:13 GMT
• Title: Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations
• Authors: David Witman, Alexander New, Hicham Alkendry, Honest Mrema
• Abstract summary: We propose an approach to solving partial differential equations (PDEs) using a set of neural networks. 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.
• Score: 63.8376359764052
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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