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.

通过引入物理和几何信息的神经操作网络，本文提出了一种应用于声波散射正向模拟的模型，该模型通过基于非均匀有理 B 样条 (NURBS) 的几何参数化方法，能够对任意形状的散射体预测散射声压场，并且具有简洁有效的表示方式，同时避免了基于物理的方法在改变计算域时需要重新评估模型的问题。数值研究结果表明，该方法具有出色的模拟任意散射体几何组合所产生的声波压力场的能力，突显了所提出的操作学习方法的独特泛化能力。