Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates

TL;DR

This paper explores neural PDE surrogates to accelerate two-phase flow simulations, extending existing methods to complex geometries, and demonstrates up to 1000x speed-up with improved accuracy in modeling oil expulsion dynamics.

Contribution

It introduces geometry-aware neural PDE solvers for complex two-phase flow problems, enhancing speed and accuracy over previous methods.

Findings

Neural PDE surrogates achieve up to 1000x speed-up.

Extensions improve performance over baseline models.

Varying geometries significantly increase problem complexity.

Abstract

Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many forward solves, for example in the case of inverse design with many degrees of freedom. In this work, we investigate and extend neural PDE solvers as a tool to aid in scaling simulations for two-phase flow problems, and simulations of oil expulsion from a pore specifically. We extend existing numerical methods for this problem to a more complex setting involving varying geometries of the domain to generate a challenging dataset. Further, we investigate three prominent neural PDE solver methods, namely the UNet, DRN, and U-FNO, and extend them for characteristics of the oil-expulsion problem: (1) spatial conditioning on the geometry; (2) periodicity in the boundary; (3) approximate mass conservation. We scale all methods and benchmark their speed-accuracy trade-off, evaluate qualitative properties, and perform an ablation study. We find that the investigated methods can accurately model the droplet dynamics with up to three orders of magnitude speed-up, that our extensions improve performance over the baselines, and that the introduced varying geometries constitute a significantly more challenging setting over the previously considered oil expulsion problem.