用可微物理模型重建声场，数据极少时也更准更快。
Differentiable physics for sound field reconstruction
- 用神经网络拟初值，可微数值求解器算波传播。
- 极端少样本下仍高精度，收敛性优于传统方法。
- 适合传感器稀疏场景的声场重建，如智能音箱部署。
声场重建旨在从有限空间分布的观测中估计声场。本文提出一种可微物理方法：用神经网络逼近波动方程的初始条件，通过可微数值求解器计算微分算子。与传统物理信息神经网络（PINN）将物理约束加入损失函数不同，该方法将物理作为强约束，确保训练稳定。此外引入稀疏性促进约束，在严重欠采样条件下也能获得有意义解。实验表明，该方法在极端数据稀缺情况下仍能实现更高精度和更好收敛性，优于现有PINN方法。
原文摘要 · Abstract (English)
Sound field reconstruction involves estimating sound fields from a limited number of spatially distributed observations. This work introduces a differentiable physics approach for sound field reconstruction, where the initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. The use of a numerical solver enables a stable network training while enforcing the physics as a strong constraint, in contrast to conventional physics-informed neural networks, which include the physics as a constraint in the loss function. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity, achieving higher accuracy and better convergence compared to physics-informed neural networks.
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