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

TL;DR

MRPARCv2 introduces a multi-resolution, physics-aware recurrent convolutional framework that embeds advection–diffusion–reaction structure to model complex turbulent flows. By operating across three resolutions and facilitating cross-scale feature exchange, it achieves substantial gains over a single-resolution baseline in VRMSE and physics-driven metrics, including TKE spectra and mass–temperature distributions, while using ~30% fewer parameters. The work also explores learning the equation of state, variable substitution effects, and early-stage uncertainty quantification, revealing that embedding EOS knowledge is critical for physical fidelity. Collectively, the results demonstrate that multi-resolution inductive bias enhances multi-scale flow modeling and point to EOS embedding as a promising area for future physics-informed ML development.

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.

Figures (16)

• Figure 1: Architecture diagram of MRPARCv2. Standard rectangles denote modules, while rounded rectangles represent inputs, outputs, and intermediate tensors. The number of resolution levels and the number of channels per resolution level are indicated for both module outputs and tensors. Refer to \ref{['fig:modules']} for the diagram of each module.
• Figure 2: Module diagram of MRPARCv2. Standard rectangles denote modules, while rounded rectangles represent inputs, outputs, and intermediate tensors. The number of resolution levels and the number of channels per resolution level are indicated for both module outputs and tensors.
• Figure 3: Ground truth and roll-out prediction of density field of $t_{cool}$ = 0.32
• Figure 4: Ground truth and roll-out prediction of pressure field of $t_{cool}$ = 0.32
• Figure 5: Ground truth and roll-out prediction of X velocity field of $t_{cool}$ = 0.32