Application of differentiable programming to wave simulation

Abstract

Wave simulations play a crucial role in a wide range of scientific and engineering applications, including seismic imaging, optical design, and acoustic modeling. Here we explore the advantages of differentiable programming in the context of acoustic wave simulation. Differentiable programming enables us to treat wave simulation as a differentiable function, allowing for the automatic computation of gradients with respect to any continuous input parameter. We demonstrate how this approach can be applied to various types of wave simulations, such as Pseudo-spectral time-domain solvers or iterative solvers. Implementing wave simulators via differentiable programming achieves several benefits. First, it enables efficient and accurate sensitivity analysis: This is particularly valuable for optimization and uncertainty quantification tasks. Second, it facilitates the incorporation of wave simulations into machine learning frameworks, enabling the integration of simulation-based models with data-driven approaches. Third, differentiable programming can accelerate the calibration and inversion of wave simulation models, making it easier to match simulated results to observed data. We present practical examples and discuss potential applications in fields such as geophysics and medical imaging. Our findings highlight the potential of this approach to advance the state-of-the-art in wave simulation techniques and their integration into larger computational pipelines.