Physics-Informed Shearlet Neural Operator (PI-ShearletNO) for parametric partial differential equations

Fabio Pereira dos Santos, Júlio de Castro Vargas Fernandes, Adriano M A Cortes

Keywords: Shearlets Transformation, Shearlet Neural Operator, Neural Operator, Physics-informed Neural Operator

TL;DR: This paper introduces the Physics-Informed Shearlet Neural Operator (PI-ShearletNO).

Abstract: This paper introduces the Physics-Informed Shearlet Neural Operator (PI-ShearletNO), a framework for learning solution operators of parametric partial differential equations. The model combines neural operator learning with the geometric sensitivity of shearlet transforms, which provide a multiscale and directional representation. By embedding the governing physical laws directly into the learning objective as constraints, PI-ShearletNO produces predictions that fit observed data while remaining consistent with the underlying PDE and boundary conditions. This physics-informed formulation improves generalization and accuracy compared with purely data-driven operator learning. We demonstrate the efficacy of PI-ShearletNO through numerical experiments on benchmark problems, highlighting both accuracy and computational efficiency when learning mappings between function spaces.

Submission Number: 102