DiffTopo: Solver in the Loop for Inverse Topography via Condition Diffusion Generation

Abstract: Inferring seabed topography from wave height observations is fundamental to tsunami hazard assessment, coastal planning, and large scale ocean circulation modeling. Classical inversion models typically rely on direct sensing or optimization based schemes that must contend with the strongly nonlinear coupling between free surface dynamics and topography. However, data driven approaches are capable of tackling strongly nonlinear problems by learning the underlying data distributions. This study introduces DiffTopo, a conditional diffusion model that reconstructs topography from surface wave field data governed by shallow water equations. Leveraging classifier free guidance, DiffTopo not only generates a series of solutions but also applies a thresholding mechanism that ensures, via the solver, the validation results are physically plausible. This study evaluates both observed wave fields and three distinct topography configurations, demonstrating that DiffTopo exhibits robust generalization and remains consistent with the shallow water equations even under full observations. These results underscore the potential of diffusion based generative modeling for addressing ill posed inverse problems in geophysics.