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

• URL: http://arxiv.org/abs/2511.11415v1
• Date: Fri, 14 Nov 2025 15:46:05 GMT
• Title: Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization
• Authors: Nikolas Borrel-Jensen, Josiah Bjorgaard,
• Abstract summary: We show that JAX-FEM's automatic differentiation (AD) enables direct gradient-based estimation of complex boundary admittance from sparse pressure measurements.<n>We apply randomized finite differences to acoustic shape optimization, combining JAX-FEM for forward simulation with PyTorch3D for mesh manipulation through AD.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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