Physics and geometry informed neural operator network with application to acoustic scattering

TL;DR

This paper presents a physics and geometry informed neural operator network that efficiently predicts acoustic scattering from arbitrarily shaped objects, significantly reducing computation time and eliminating the need for labeled training data.

Contribution

The paper introduces a novel physics-informed deep operator network using NURBS for geometric parameterization, enabling fast, generalizable acoustic scattering simulations without labeled data.

Findings

Achieves rapid prediction of scattered pressure fields for arbitrary shapes.

Reduces computational time by orders of magnitude compared to traditional solvers.

Demonstrates strong generalization to various geometries in numerical studies.

Abstract

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution operator for different computational domains is a problem of general importance for a variety of engineering applications. To this end, we propose a physics-informed deep operator network (DeepONet) capable of predicting the scattered pressure field for arbitrarily shaped scatterers using a geometric parameterization approach based on non-uniform rational B-splines (NURBS). This approach also results in parsimonious representations of non-trivial scatterer geometries. In contrast to existing physics-based approaches that require model re-evaluation when changing the computational domains, our trained model is capable of learning solution operator that can approximate physically-consistent scattered pressure field in just a few seconds for arbitrary rigid scatterer shapes; it follows that the computational time for forward simulations can improve (i.e. be reduced) by orders of magnitude in comparison to the traditional forward solvers. In addition, this approach can evaluate the scattered pressure field without the need for labeled training data. After presenting the theoretical approach, a comprehensive numerical study is also provided to illustrate the remarkable ability of this approach to simulate the acoustic pressure fields resulting from arbitrary combinations of arbitrary scatterer geometries. These results highlight the unique generalization capability of the proposed operator learning approach.