Making the most of Differentiable Propagators for Small-Angle X-ray Scattering (SAXS)

Understanding laser-solid interactions is important for the development of laser-driven particle and photon sources, e.g., tumor therapy, astrophysics, and fusion. Currently, these interactions can only be modeled by simulations that need to be verified experimentally. Consequently, pump-probe experiments were conducted to examine the laser-plasma interaction that occurs when a high intensity laser hits a solid target. Since we aim for a femtosecond temporal and nanometer spatial resolution at European XFEL, we employ Small-Angle X-ray Scattering (SAXS) and Phase Contrast Imaging (PCI) that can each be approximated by an analytical propagator. In our reconstruction of the target, we employ gradient descent (GD) to iteratively minimize the error between experimental and synthetic patterns propagated from proposed target structures. By implementing the propagator in PyTorch, we leverage the automatic differentiation and GPU acceleration for the GD fit and at the same time obtain a differentiable physically-based loss function for unsupervised training of inversion or surrogate models. For a classical fit, we sample many different initial values for parameters, such as target asymmetry, to find the global minimum, leveraging batch-parallelism. A data-driven model to predict initial conditions close to actual minima can be trained in an unsupervised manner using our pipeline.