Wave propagation is ubiquitous in physical phenomena. Mathematically, Fourier and microlocal methods serve as robust tools for elucidating the analytical and geometric structures of wave propagation. However, wave propagation in numerical simulation and inversion remains highly challenging in both traditional computational mathematics and machine learning, owing to the highly oscillatory nature of waves and the complexity of propagation media. The integration of Fourier and microlocal methods into computational wave propagation proves useful in reducing computational cost. This talk shall discuss several existing works and recent advances from this perspective.
