# A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

arXiv: https://arxiv.org/abs/2607.00460 · HTML: https://mlsanity.com/paper/2607.00460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [Differentiable hybrid neural modeling for fluid-structure interaction](https://mlsanity.com/paper/2303.12971/) (2023)
- [P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics](https://mlsanity.com/paper/2411.00040/) (2024)
- [Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flows](https://mlsanity.com/paper/2507.01975/) (2025)

## Abstract (arXiv)

Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters. An effective approach to address these challenges is leveraging physics priors in training neural networks, known as physics-informed deep learning (PiDL). In this work, we introduce the Multi-Resolution Finite-Volume-inspired network, MuRFiV, designed to capitalize on the conservative property of finite volume on the global scale and the expressive power of deep learning on the local scale. We demonstrate the effectiveness of MuRFiV on several spatio-temporal systems governed by partial differential equations (PDEs), including Burgers' equation, shallow water equations, and incompressible Navier-Stokes equations. By embedding PDE information into the deep learning architecture, MuRFiV achieves strong long-term prediction accuracy and remains stable over very long autoregressive rollouts, significantly outperforming data-driven neural network baselines. This result highlights the promise of combining multiresolution learning with finite-volume-inspired inductive bias for accurate and robust long-term prediction of complex dynamics.