Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization

TL;DR

This paper presents a differentiable programming approach for acoustic inverse problems, enabling efficient admittance estimation and shape optimization through automatic differentiation and finite differences, significantly reducing computational effort.

Contribution

It introduces a practical differentiable framework combining JAX-FEM and PyTorch3D for acoustic inverse problems, streamlining gradient-based estimation and shape optimization.

Findings

Achieved 3-digit precision in admittance estimation from sparse data.

Reduced energy at target frequencies by 48.1% with fewer FEM solutions.

Demonstrated 30-fold reduction in FEM computations compared to standard methods.

Abstract

We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic differentiation (AD) enables direct gradient-based estimation of complex boundary admittance from sparse pressure measurements, achieving 3-digit precision without requiring manual derivation of adjoint equations. Second, we apply randomized finite differences to acoustic shape optimization, combining JAX-FEM for forward simulation with PyTorch3D for mesh manipulation through AD. By separating physics-driven boundary optimization from geometry-driven interior mesh adaptation, we achieve 48.1% energy reduction at target frequencies with 30-fold fewer FEM solutions compared to standard finite difference on the full mesh. This work showcases how modern differentiable software stacks enable rapid prototyping of optimization workflows for physics-based inverse problems, with automatic differentiation for parameter estimation and a combination of finite differences and AD for geometric design.