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Stochastic partial differential equations (SPDEs) are significant tools formodeling dynamics in many areas including atmospheric sciences and physics.Neural Operators, generations of neural networks with capability of learningmaps between infinite-dimensional spaces, are strong tools for solvingparametric PDEs. However, they lack the ability to modeling SPDEs which usuallyhave poor regularity due to the driving noise. As the theory of regularitystructure has achieved great successes in analyzing SPDEs and provides theconcept model feature vectors that well-approximate SPDEs' solutions, wepropose the Neural Operator with Regularity Structure (NORS) which incorporatesthe feature vectors for modeling dynamics driven by SPDEs. We conductexperiments on various of SPDEs including the dynamic Phi41 model and the 2dstochastic Navier-Stokes equation, and the results demonstrate that the NORS isresolution-invariant, efficient, and achieves one order of magnitude lowererror with a modest amount of data.

Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs