A Differentiable Forward Model for Physics-Based Inverse Problems in SAR Imaging

Sammanfattning

Differentiable physics-based forward models have emerged as a key component in scientific machine learning (SciML) approaches to inverse problems, where physical simulators are embedded directly into machine learning and optimization pipelines. In such approaches, gradients are propagated through the forward model itself, allowing learned components to remain grounded in the physics. In this thesis, we develop a differentiable forward model for synthetic aperture radar (SAR) that maps a three-dimensional scene representation to complex radar data, with the explicit goal of enabling future work on gradient-based SciML pipelines for SAR reconstruction. The model uses a ray-based formulation under a weak scattering Born approximation, enabling visibility, object occlusion, surface incidence, and antenna beam effects to be modeled directly in three-dimensional scene space. The implementation is designed for GPU execution and computational efficiency, allowing large numbers of rays and fine mesh resolutions to be evaluated within a differentiable optimization pipeline. The operator is validated through a series of controlled experiments that test point-target responses, resolution in range, operator linearity, antenna-pattern behavior, and convergence with respect to the main discretization parameters, demonstrating that the simulated measurements are consistent with expected SAR signal physics. The differentiability of the model is further evaluated through reconstruction experiments. Reflectivity reconstruction experiments show stable reduction of the data misfit, and geometry reconstruction experiments on a simplified scene demonstrate that a height map representation of the scene can be accurately recovered directly from complex SAR measurements. Together, these results indicate that the proposed operator provides a viable and differentiable building block for SciML-based SAR reconstruction.