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

2025-12-04

AI Summary

In multi-scale flow simulation, accuracy degrades due to the absence of equation-of-state physical constraints, while conventional methods struggle to balance computational efficiency and predictive fidelity. Method: We propose a physics-embedded multi-resolution neural operator that explicitly encodes the structure of convection–diffusion–reaction equations into its architecture. It integrates hierarchical discretization, cross-resolution feature communication, and physics-aware recurrent convolution, and is trained and validated using variance-scaled error metrics and turbulence kinetic energy spectra as physically grounded objectives. Results: Compared to single-resolution baselines, our model reduces parameter count by 30%, achieves a 50% reduction in rollout prediction error, and lowers spectral error by 86% on 2D turbulent radiative layer data—demonstrating the effectiveness and generalization advantage of multi-resolution inductive bias for complex flow modeling.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Modeling complex flows with multi-resolution physics-aware neural networks
• Improving accuracy and efficiency in turbulent flow simulations
• Embedding physical constraints to enhance model fidelity

Innovation

• Multi-resolution architecture with hierarchical discretization
• Embedding advection-diffusion-reaction equation structure
• Cross-resolution feature communication for accuracy