Learning Time-Aware Assistance Functions for Numerical Fluid Solvers
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.
We introduce a neural network approach to assist partial differential equation solvers.The authors aim at improving the accuracy of numerical solvers by training a neural network on simulated reference data which corrects the numerical solver.