Physics informed WNO
This addresses the data efficiency problem for researchers and practitioners using neural operators to solve parametric PDEs in engineering and science, though it appears incremental as it extends an existing WNO framework.
The authors tackled the data-hungry nature of Wavelet Neural Operators (WNO) for learning PDE solution operators by proposing a physics-informed WNO that eliminates the need for labeled training data, demonstrating its effectiveness on four nonlinear spatiotemporal systems relevant to engineering and science.
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. 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. 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.