Learning subgrid interfacial area in two-phase flows with regime-dependent inductive biases

TL;DR

This paper develops and compares physics-informed and purely data-driven machine learning models to predict subgrid interfacial area density in turbulent multiphase flows, highlighting the importance of regime-dependent inductive biases.

Contribution

It introduces a physics-constrained model with a fractal geometric prior and demonstrates its regime-dependent effectiveness in improving predictions over purely data-driven models.

Findings

Physics-based model improves accuracy and reduces artifacts.

Regime-dependent effectiveness of inductive biases in modeling.

Embedded biases enhance generalization in certain flow regimes.

Abstract

The reliability of machine learning in multiscale physical systems depends on how physical structure is embedded into the learning process. We investigate this in the context of turbulent multiphase flows, focusing on the prediction of subgrid interfacial area density, a key quantity governing interphase transport that remains unresolved in large-eddy simulations. In this work, we develop and evaluate two machine learning subgrid closure models to predict the three-dimensional subgrid interfacial area density: a purely data-driven 3D encoder-decoder network, and a physics-constrained variant regularized by a fractal geometric prior. Across a range of Weber numbers, the physics-based model improves predictive accuracy, reduces error variance, and suppresses nonphysical artifacts relative to purely data-driven approaches. We also show that these gains are regime-dependent: the embedded inductive bias enhances generalization in corrugation-dominated regimes where its underlying assumptions hold, but becomes ineffective in fragmentation-dominated regimes characterized by topology change and droplet breakup. These results reveal a broader principle for scientific machine learning: the utility of physics-informed models depends not only on the presence of inductive bias, but on its alignment with the governing physical regime. This suggests a path toward regime-aware learning frameworks for modeling of complex multiscale systems.