Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates

TL;DR

This work tackles the heavy computational burden of simulating two-phase flows by developing neural PDE surrogates that autoregressively approximate time-stepping operators for oil expulsion in porous geometries. It extends three neural architectures (DRN, U-FNO, UNet) with geometry conditioning, periodic boundary handling, and approximate mass conservation, and evaluates them on datasets that include varying obstacles. The results show that neural surrogates can achieve up to three orders of magnitude speed-up while maintaining realistic droplet dynamics, with UNet offering the strongest speed-accuracy scaling. The findings highlight the potential of geometry-informed neural surrogates for rapid design, optimization, and control in complex multiphase flow problems, and point to directions such as probabilistic modeling and amortized cost analysis for real-world deployment.

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.

Figures (6)

• Figure 1: The oil expulsion problem illustrated. Top: Numerical solver reference. Bottom: Neural surrogate model (UNet) prediction.
• Figure 2: Schematic overview of model architectures.
• Figure 3: Work-precision diagrams for full rollout MSE on the test set versus the inference time of 25 timesteps (1 block), for the GPU and CPU. All models share the same general architecture with the processor parameters scaled. Parameter ranges were scanned to find ranges that scaled well w.r.t. both MSE and inference speed on the GPU; Pareto-optimal settings are plotted.
• Figure 4: Comparison of distributions with small variations of the charge parameter, for a charge of -8.65 $\pm$ 20% ($\pm$ 15 simulations). At earlier times the distributions mostly overlap, however in the final case there is a significant deviation. The multi-modal behavior -- where in some cases the droplet gets stuck on the obstacle, and in others it moves past -- is recovered in most cases, but not very precisely.
• Figure 5: Test set example with predictions of all model classes considered, using the settings within each class that led to the lowest MSE.