MuRFiV-Net: A Multi-Resolution Finite-Volume Inspired Neural Network for Predicting Spatiotemporal Dynamics

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-Net, 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-Net on several spatio-temporal systems governed by partial differential equations (PDEs), including burgers' equation, Kuramoto–Sivashinsky equation, and Navier-Stokes equation. By embedding PDE information into the deep learning architecture, MuRFiV-Net achieves superior performance in predicting spatiotemporal dynamics, surpassing data-driven neural networks. This novel approach offers a promising avenue for tackling complex dynamic systems with improved accuracy and efficiency.