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.

翻译：我们通过两个应用案例展示了一种实用的可微分编程方法用于声学反问题：共振阻尼的导纳估计和形状优化。首先，我们证明JAX-FEM的自动微分技术能够基于稀疏压力测量直接通过梯度方法估计复杂边界导纳，无需手动推导伴随方程即可实现三位数精度。其次，我们将随机有限差分法应用于声学形状优化，结合JAX-FEM进行前向仿真，并通过自动微分利用PyTorch3D进行网格操作。通过将物理驱动的边界优化与几何驱动的内部网格自适应分离，与在完整网格上采用标准有限差分法相比，我们在目标频率处实现了48.1%的能量衰减，且有限元求解次数减少了30倍。这项工作展示了现代可微分软件栈如何通过自动微分实现参数估计，并结合有限差分与自动微分进行几何设计，从而快速构建基于物理反问题的优化工作流程原型。