Physics informed WNO

Abstract

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict solutions of PDEs for varying initial or boundary conditions and different inputs without repeated independent runs from scratch. A recently proposed Wavelet Neural Operator (WNO) is one such operator that harnesses the advantage of time–frequency localization of wavelets to capture the manifolds in the spatial domain effectively. While WNO has proven to be a promising method for operator learning, the data-hungry nature of the framework is a major shortcoming. Relying completely on conventional solvers for data generation and subsequently training operators with generated data leads to a time-consuming and challenging implementation of the operators in practical applications. In this work, we propose a physics-informed WNO for learning the solution operators of families of parametric PDEs without labeled training data. The efficacy of the framework is validated and illustrated with four nonlinear spatiotemporal systems relevant to various fields of engineering and science.