Differentiable Geometric Acoustic Path Tracing using Time-Resolved Path Replay Backpropagation

Differentiable rendering has become a key ingredient in solving challenging inverse problems in computer graphics and vision. Existing systems can simulate and differentiate the spatial propagation of light. We exploit the duality of light transport simulations and geometric acoustics to apply differential rendering techniques to established acoustic simulation methods. The resulting system is capable of simulating sound according to the geometrical acoustics model and computing derivatives of the output energy spectrograms with respect to arbitrary parameters of the scene, including materials, emitters, microphones, and scene geometry. Contrary to current differentiable transient rendering, we can handle arbitrary simulation depths and achieve constant memory and linear execution times by presenting a temporal extension of Path Replay Backpropagation [Vicini et al. 2021]. We verify our model against established simulation software, and demonstrate the capabilities of optimization with gradients at examples of inverse acoustics and optimizing room parameters. This opens up a new field of research for acoustic optimization that could be as impactful for the acoustic community as differentiable rendering was for the graphics community.