用自动微分解决声学逆问题，实现高精度阻抗估计与高效结构优化。
Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization
- 基于JAX-FEM自动微分，直接从稀疏压力数据估算复杂边界阻抗。
- 在目标频率下实现48.1%能量降低，计算量仅为传统方法的1/30。
- 适合做物理驱动优化、声学设计及可微分仿真系统的研究人员。
我们展示了通过两种应用实现声学逆问题的实用可微编程方法：阻抗估计与共振抑制的形状优化。首先，利用JAX-FEM的自动微分（AD），无需手动推导伴随方程，即可从稀疏压力测量中直接进行梯度优化，实现三位数精度的复杂边界阻抗估计。其次，将随机有限差分应用于声学形状优化，结合JAX-FEM进行前向模拟与PyTorch3D进行网格操作，通过分离物理驱动的边界优化与几何驱动的内部网格适应，仅需30倍少于标准有限差分的FEM求解次数，就在目标频率下实现48.1%的能量衰减。本工作表明，现代可微软件栈可通过自动微分实现参数估计，并结合有限差分与自动微分完成几何设计，加速物理驱动逆问题的原型开发。
原文摘要 · Abstract (English)
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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