AI Insight
Researchers developed a physics-informed neural network called DeepONet that can solve the 2D Helmholtz equation for wave scattering around obstacles of arbitrary shapes. The system uses a signed distance function to encode the geometry of scatterers and learns to predict the resulting scattered wave field without requiring domain-specific meshing or parameterization. The trained model demonstrates generalization to unseen geometries and can be refined for new regions of interest without complete retraining.
Why it matters
This approach provides a computationally efficient alternative to traditional finite element methods for solving wave equations, eliminating the need to remesh domains for each new geometry. The framework has potential applications in acoustic and electromagnetic wave simulations, structural analysis, and other fields requiring rapid solutions to wave propagation problems across varying geometries.
Understand the Science
Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary geometry at its center. It acts as a scatterer for an incoming harmonic wave. The aim is to learn the operator linking the geometry of the scatterer to the resulting scattered field. A signed distance function to the boundary of the inner inclusion evaluated in several points on the domain is used to encode its geometry. It serves as input for the branch part of the DeepONet architecture and local information as the input for the trunk part. This approach enables the encoding of arbitrary geometries, whether they are parameterized or not. The evaluation of the model on unseen geometries was compared to its finite element method (FEM) equivalent to test its generalization capabilities. The trained network weights implicitly embed the local physics and their interaction with the domain geometry. If the training space sufficiently covers the target evaluation space, the model can generalize accordingly. Furthermore, it can be refined to extend to another region of interest without retraining from scratch. This framework also avoids the need to remesh the domain for each geometry. The proposed approach delivers a computationally lighter surrogate model than FEM alternatives and avoids relying on FEM generated training data.
Source: Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries