Fill the gaps: continuous in time interpolation of fluid dynamical simulations

TL;DR

This paper introduces a physics-informed machine learning model combining PITT and FNO for fluid simulation interpolation, achieving high accuracy with less data and conserving physical quantities.

Contribution

The paper develops a novel PITT FNO network for fluid data interpolation, demonstrating improved efficiency and physical conservation over traditional methods.

Findings

Requires 6-10 times less data than linear interpolation

Maintains excellent mass and energy conservation

Can recover fine details with spectral analysis

Abstract

Flexible and accurate interpolation schemes using machine learning could be of great benefit for many use-cases in numerical simulations and post-processing, such as temporal upsampling or storage reduction. In this work, we adapt the physics-informed token transformer (PITT) network for multi-channel data and couple it with Fourier neural operator (FNO). The resulting PITT FNO network is trained for interpolation tasks on a dataset governed by the Euler equations. We compare the performance of our machine learning model with a linear interpolation baseline and show that it requires $\sim6-10$ times less data to achieve the same mean square error of the interpolated quantities. Additionally, PITT FNO has excellent mass and energy conservation as a result of its physics-informed nature. We further discuss the ability of the network to recover fine detail using a spectral analysis. Our results suggest that loss of fine details is related to the decreasing correlation time of the data with increasing Fourier mode which cannot be resolved by simply increasing Fourier mode truncation in FNO.