Greedy Optimal Sampling via Variably Scaled Kernels for Solar Inverse Problems

Speaker: Prof. Emma Perracchione, Politecnico di Torino

Abstract: We present a comprehensive framework for solving high-dimensional inverse problems in solar physics using adaptive kernel-based methods. This approach integrates Variably Scaled Kernels (VSKs) with greedy sampling strategies, enabling efficient reconstruction of solar phenomena from sparse, noisy observational data. VSKs utilize spatially-varying scale functions to adapt the shape of basis 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 adaptive method achieves comparable or superior accuracy to leading approaches while reducing computational costs and the number of basis functions required.

Biography: Emma Perracchione is associate professor at the Politecnico di Torino, and she leads several research projects in numerical methods and applied analysis. She specializes in adaptive sampling techniques and approximation theory for inverse problems. She actively engages in the academic community through conferences and collaborations, contributing significantly to advancements in mathematical methodologies.

Host: Prof. Michael Multerer