2022/04/13 by Peiyan Hu, Meng Qi, Hu, Peiyan +15 · 1 citation
Computer Science · Environmental Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Hydrological Forecasting Using AI #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2204.06255
openalex publication_date 2022/04/13 · openalex created_date 2022/04/27 · openalex updated_date 2026/07/28
Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps between infinite-dimensional spaces, are strong tools for solving parametric PDEs. However, they lack the ability to modeling SPDEs which usually have poor regularity due to the driving noise. As the theory of regularity structure has achieved great successes in analyzing SPDEs and provides the concept model feature vectors that well-approximate SPDEs' solutions, we propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d stochastic Navier-Stokes equation, and the results demonstrate that the NORS is resolution-invariant, efficient, and achieves one order of magnitude lower error with a modest amount of data.