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arXiv · 2511.11415

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

Nikolas Borrel-Jensen·Josiah Bjorgaard
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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.

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Nikolas Borrel-Jensen, Josiah Bjorgaard. 2025-11-14. Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization. https://arxiv.org/abs/2511.11415

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