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

arXiv: https://arxiv.org/abs/2512.06031 · HTML: https://mlsanity.com/paper/2512.06031/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Overview frequency principle/spectral bias in deep learning](https://mlsanity.com/paper/2201.07395/) (2022)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Hamiltonian neural networks for solving equations of motion](https://mlsanity.com/paper/2001.11107/) (2020)
- [Grasping Extreme Aerodynamics on a Low-Dimensional Manifold](https://mlsanity.com/paper/2305.08024/) (2023)
- [Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression](https://mlsanity.com/paper/2109.08248/) (2021)
- [Artificial intelligence approaches for materials-by-design of energetic materials: state-of-the-art, challenges, and future directions](https://mlsanity.com/paper/2211.08179/) (2022)
- [Low-Order Flow Reconstruction and Uncertainty Quantification in Disturbed Aerodynamics Using Sparse Pressure Measurements](https://mlsanity.com/paper/2501.03406/) (2025)
- [A physics-aware deep learning model for shear band formation around collapsing pores in shocked reactive materials](https://mlsanity.com/paper/2510.09670/) (2025)

## Built on by (most cited first, 1 of 1)

- [G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes](https://mlsanity.com/paper/2604.16533/) (2026)

## Abstract (arXiv)

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.