Physics informed WNO

TL;DR

This paper introduces a physics-informed Wavelet Neural Operator (WNO) that learns solution operators of parametric PDEs without labeled data, leveraging physics constraints to improve efficiency and applicability.

Contribution

It proposes a novel physics-informed WNO framework that reduces data requirements for operator learning of PDEs, validated on multiple nonlinear systems.

Findings

Effective in learning solution operators without labeled data

Validated on four nonlinear spatiotemporal systems

Demonstrates improved data efficiency over traditional 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. 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.