Acoustic field estimation with differentiable physics

This work introduces a differentiable physics approach to estimate acoustic fields from a limited number of spatially distributed observations. The initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Numerical experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity.