Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flows

Abstract: We present MRPARCv2, Multi-resolution Physics-Aware Recurrent Convolutional Neural Network, designed to model complex flows by embedding the structure of advection-diffusion-reaction equations and leveraging a multi-resolution architecture. MRPARCv2 introduces hierarchical discretization and cross-resolution feature communication to improve the accuracy and efficiency of flow simulations. We evaluate the model on a challenging 2D turbulent radiative layer dataset from The Well multi-physics benchmark repository and demonstrate significant improvements when compared to the single resolution baseline model, in both Variance Scaled Root Mean Squared Error and physics-driven metrics, including turbulent kinetic energy spectra and mass-temperature distributions. Despite having 30% fewer trainable parameters, MRPARCv2 outperforms its predecessor by up to 50% in roll-out prediction error and 86% in spectral error. A preliminary study on uncertainty quantification was performed, and we also analyzed the model's performance under different levels of abstractions of the flow, specifically on sampling subsets of field variables. We find that the absence of physical constraints on the equation of state (EOS) in the network architecture leads to degraded accuracy. A variable substitution experiment confirms that this issue persists regardless of which physical quantity is predicted directly. Our findings highlight the advantages of multi-resolution inductive bias for capturing multi-scale flow dynamics and suggest the need for future PIML models to embed EOS knowledge to enhance physical fidelity.