Physics-informed neural networks for solving moving interface flow problems using the level set approach

TL;DR

This paper demonstrates that physics-informed neural networks, especially PirateNet architecture, can effectively solve complex moving interface flow problems using the level set method, achieving high accuracy without traditional stabilization techniques.

Contribution

The study adapts PirateNet's features for level set problems, showing improved accuracy and stability in simulating moving interfaces compared to conventional PINNs.

Findings

Achieved state-of-the-art error rates of 0.14% and 0.85% in benchmark problems.

PINNs can handle significant interface deformation without upwind stabilization.

Embedded geometric reinitialization enhances long-term stability in complex two-phase flows.

Abstract

This paper advances the use of physics-informed neural networks (PINNs) architectures to address moving interface problems via the level set method. Originally developed for other PDE-based problems, we particularly leverage PirateNet's features, including causal training, sequence-to-sequence learning, random weight factorization, and Fourier feature embeddings, and tailor them to handle problems with complex interface dynamics. Numerical experiments validate this framework on benchmark problems such as Zalesak's disk rotation and time-reversed vortex flow. We demonstrate that PINNs can efficiently solve level set problems exhibiting significant interface deformation without the need for upwind numerical stabilization, as generally required by classic discretization methods, or additional mass conservation schemes. However, incorporating an Eikonal regularization term in the loss function with an appropriate weight can further enhance results in specific scenarios. Our results indicate that PINNs with the PirateNet architecture surpass conventional PINNs in accuracy, achieving state-of-the-art error rates of $L^2=0.14\%$ for Zalesak's disk and $L^2=0.85 \%$ for the time-reversed vortex flow problem, as compared to reference solutions. Additionally, for a complex two-phase flow dam break problem coupling the level set with the Navier-Stokes equations, we propose a geometric reinitialization method embedded within the sequence-to-sequence training scheme to ensure long-term stability and accurate inference of the level set field.