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

2026-07-01

AI Summary

This work addresses the challenges of predicting complex spatiotemporal dynamics—namely high computational cost, error accumulation, and limited generalization—by introducing the MuRFiV framework. MuRFiV innovatively incorporates the global conservation property of the finite volume method as a physics-informed inductive bias within a multi-resolution deep neural architecture, effectively integrating physical priors with data-driven representational capacity. By synergistically combining physics-informed learning, multiscale modeling, and autoregressive rollout prediction, the proposed method achieves significantly higher accuracy and long-term stability compared to purely data-driven baselines across benchmark systems, including the Burgers equation, shallow water equations, and incompressible Navier–Stokes equations.

Abstract

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.

Problem

• spatiotemporal dynamics
• physics-informed deep learning
• partial differential equations
• long-term prediction
• generalizability

Innovation

• physics-informed deep learning
• finite-volume method
• multi-resolution learning
• spatiotemporal dynamics
• PDE-constrained modeling