Mapping-based Hard-constrained Physics-Informed Neural Networks for unbounded wave problems

TL;DR

This paper introduces MH-PINN, a novel neural network approach that uses coordinate mapping and hard constraints to efficiently solve unbounded wave problems with high accuracy.

Contribution

It proposes a mapping technique to handle unbounded domains and a physics-based hard-constrained structure that improves efficiency and convergence in wave simulations.

Findings

Successfully solves acoustic and elastic wave problems with high accuracy.

Reduces computational cost by eliminating boundary loss terms.

Demonstrates robustness across various wave scenarios.

Abstract

The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that compactifies the infinite physical domain into a finite computational space. This effectively resolves the sampling difficulties inherent to standard PINNs in unbounded regions. Additionally, it avoids the artificial truncation errors introduced by traditional methods such as perfectly matched layers. Second, we design a physics-based hard-constrained network structure that automatically satisfies both the inner boundary conditions and the far-field radiation conditions. This structure eliminates boundary loss terms, yielding high computational efficiency and fast convergence, which effectively addresses the challenges of high-frequency problems. Third, we introduce an inverse factor correction for boundary coefficients to address the influence of asymptotic factors,which makes the method highly geometrically adaptable. Finally, we present numerical examples covering various acoustic radiation and scattering scenarios as well as elastic dynamics scenarios to demonstrate the efficiency and accuracy of our algorithm.It highlights its potential for broader applications in the field of computational wave dynamics.