Abstract: We present a framework for solving inverse problems in solar physics using adaptive kernel-based methods. This approach combines Variably Scaled Kernels (VSKs) with greedy sampling strategies, enabling efficient reconstruction of solar phenomena from sparse, noisy data. VSKs adapt the shape of basis functions using spatially varying scale functions, enhancing resolution in areas with rapid variations while simplifying smoother regions. The greedy algorithm features an automatic stopping criterion based on Stein's Unbiased Risk Estimate (SURE), balancing approximation accuracy with model complexity without needing the true solution. Theoretical analysis confirms convergence rates and error bounds for the greedy VSK approximation. Numerical tests on STIX flare data show that this method achieves comparable or superior accuracy to leading approaches while reducing computational costs.

Host: Prof. Michael Multerer