Differentiable physics for acoustic inverse problems

Inverse problems in acoustics are often ill-posed and subject to data scarcity. Physics-informed neural networks (PINNs) offer a promising framework to solve such problems due to their flexibility and data efficiency. However, the stiffness of the differential operators that appear in their loss function make PINNs difficult to train. In this study, we present a differentiable physics approach (DP) that integrates a differentiable numerical solver into the training of neural networks. The unknowns to be estimated (such as the initial or boundary conditions, or the wave speed) are approximated with a neural network, while the physics of wave propagation are computed using a stable FDTD solver. A series of numerical experiments demonstrate that the proposed DP can estimate unknown parameters even under extreme undersampling conditions. This work highlights the potential of combining numerical solvers with deep learning for solving complex, data-scarce acoustic problems.