Compute-Optimal Solutions for Acoustic Wave Equation Using Hard-Constraint PINNs

Chen Gu, ZHUOYU CHEN

Keywords: compute-optimal, acoustic wave equation, hard-constraint, PINN

TL;DR: This paper investigates the optimal imposition of hard constraints, the strategic sampling of PDEs, and the scaling of computational domains for solving the acoustic wave equation within a specified computational budget.

Abstract: This paper explores the optimal imposition of hard constraints, strategic sampling of PDEs, and computational domain scaling for solving the acoustic wave equation within a specified computational budget. First, we derive a formula to systematically enforce hard boundary and initial conditions in Physics-Informed Neural Networks (PINNs), employing continuous functions within the PINN ansatz to ensure that these conditions are satisfied. We demonstrate that optimally selecting these functions significantly enhances the convergence of the solution. Secondly, we introduce an importance sampling strategy that optimizes the efficiency of hard-constraint PINNs under a fixed number of sampling points. Leveraging these strategies, we develop an algorithm to determine the optimal computational domain size, given a computational budget. Our approach offers a practical framework for domain decomposition in large-scale implementation of acoustic wave equation systems.

Primary Area: Machine learning for physical sciences (for example: climate, physics)

Submission Number: 7443