Pseudo-Differential Integral Operator for Learning Solution Operators of Partial Differential Equations. (arXiv:2201.11967v1 [cs.LG])

Web: http://arxiv.org/abs/2201.11967

Learning mapping between two function spaces has attracted considerable
research attention. However, learning the solution operator of partial
differential equations (PDEs) remains a challenge in scientific computing.
Therefore, in this study, we propose a novel pseudo-differential integral
operator (PDIO) inspired by a pseudo-differential operator, which is a
generalization of a differential operator and characterized by a certain
symbol. We parameterize the symbol by using a neural network and show that the
neural-network-based symbol is contained in a smooth symbol class. …

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