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

Nikolas Borrel-Jensen, Josiah Bjorgaard

Keywords: Automatic Differentiation, Acoustics, Room Acoustics, FEM, Helmholtz, Scientific Machine Learning, Differentiable Solver, Differentiable Geometry

TL;DR: Practical differentiable programming approach for acoustic inverse problems

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 times fewer FEM solutions compared to standard finite differences. 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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Submission Number: 45