A Deep Finite Difference Emulator for the Fast Simulation of Coupled Viscous Burgers' Equation

TL;DR

This paper introduces a physics-informed deep learning emulator that mimics a finite difference solver for the viscous Burgers' equation, enabling fast and accurate simulations without traditional numerical data collection.

Contribution

The novel approach integrates finite difference schemes into a deep learning model, eliminating the need for classical solver-based training data for simulating coupled viscous Burgers' equations.

Findings

High accuracy in emulating finite difference solutions

Good generalization to different initial conditions

Significant reduction in computational time

Abstract

This work proposes a deep learning-based emulator for the efficient computation of the coupled viscous Burgers' equation with random initial conditions. In a departure from traditional data-driven deep learning approaches, the proposed emulator does not require a classical numerical solver to collect training data. Instead, it makes direct use of the problem's physics. Specifically, the model emulates a second-order finite difference solver, i.e., the Crank-Nicolson scheme in learning dynamics. A systematic case study is conducted to examine the model's prediction performance, generalization ability, and computational efficiency. The computed results are graphically represented and compared to those of state-of-the-art numerical solvers.