Past rewinding of fluid dynamics from noisy observation via physics-informed neural computing

Abstract

Reconstructing the past of observed fluids has been known as an ill-posed problem due to both numerical and physical challenges, especially when observations are distorted by inevitable noise, resolution limits, or unknown factors. When employing traditional differencing schemes to reconstruct the past, the computation often becomes highly unstable or diverges within a few backward time steps from the distorted and noisy observation. Although several techniques have been recently developed for inverse problems, such as adjoint solvers and supervised learning, they are also unrobust against errors in observation when there is time-reversed simulation. Here we present that by using physics-informed neural computing, robust time-reversed fluid simulation is possible. By seeking a solution that closely satisfies the given physics and observations while allowing for errors, it reconstructs the most probable past from noisy observations. Our work showcases time rewinding in extreme fluid scenarios such as shock, instability, blast, and magnetohydrodynamic vortex. Potentially, this can be applied to trace back the interstellar evolution and determining the origin of fusion plasma instabilities.