A deep learning approach for adaptive zoning

TL;DR

This paper introduces a supervised deep learning method that adaptively relocates computational grid points in 1D shock wave simulations, significantly reducing computational time while maintaining accuracy.

Contribution

It presents a novel DL-based adaptive zoning technique trained on shock profiles, improving efficiency over traditional methods without loss of accuracy.

Findings

DL model accurately detects shocks and adapts meshes in real-time

Reduces computational time by at least 2 times compared to standard methods

Maintains high accuracy of physical quantity reconstructions

Abstract

We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset composed of different static shock profiles associated with the corresponding adapted meshes computed with standard adaptive zoning techniques. We show that the trained DL model learns how to capture the presence of shocks in the domain and generates at each time step an adapted non-uniform mesh that relocates the grid nodes to improve the accuracy of Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space discretization schemes. We also show that the surrogate DL model reduces the computational time to perform adaptive zoning by at least a 2x factor with respect to standard techniques without compromising the accuracy of the reconstruction of the physical quantities of interest.