Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization
This work addresses acoustic design optimization for engineers, offering a practical and efficient approach, though it is incremental in applying existing differentiable tools to specific problems.
The paper tackled acoustic inverse problems by applying differentiable programming to admittance estimation and shape optimization, achieving 3-digit precision in admittance estimation and a 48.1% energy reduction in resonance damping with 30-fold fewer FEM solutions.
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.