Learning Time-Aware Assistance Functions for Numerical Fluid Solvers

Kiwon Um, Yun (Raymond) Fei, Philipp Holl, Nils Thuerey

Keywords: PDEs, convolutional neural networks, numerical simulation, fluids

TL;DR: We introduce a neural network approach to assist partial differential equation solvers.

Abstract: Improving the accuracy of numerical methods remains a central challenge in many disciplines and is especially important for nonlinear simulation problems. A representative example of such problems is fluid flow, which has been thoroughly studied to arrive at efficient simulations of complex flow phenomena. This paper presents a data-driven approach that learns to improve the accuracy of numerical solvers. The proposed method utilizes an advanced numerical scheme with a fine simulation resolution to acquire reference data. We, then, employ a neural network that infers a correction to move a coarse thus quickly obtainable result closer to the reference data. We provide insights into the targeted learning problem with different learning approaches: fully supervised learning methods with a naive and an optimized data acquisition as well as an unsupervised learning method with a differentiable Navier-Stokes solver. While our approach is very general and applicable to arbitrary partial differential equation models, we specifically highlight gains in accuracy for fluid flow simulations.