2022/07/28 by Michael Rotman, Rotman, Michael, Amit Dekel +7 · 2 citations
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #High Energy Physics - Theory (hep-th) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2207.14366
openalex publication_date 2022/07/28 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. Our method treats time and space separately. As a result, it successfully propagates initial conditions in continuous time steps by employing the general composition properties of the partial differential operators. Following previous work, supervision is provided at a specific time point. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.