BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nikolaos Pallikarakis (National Technical University of Athens) DTSTART:20240326T130000Z DTEND:20240326T140000Z DTSTAMP:20260526T055428Z UID:inverseproblems/19 DESCRIPTION:Title: Exploring Inverse Eigenvalue Problems through Machine Learning\nby Nikolaos Pallikarakis (National Technical University of Athens) as p art of Seminars on Inverse Problems Theory and Applications\n\n\nAbstract\ nThe latest years\, machine learning has been one of the main directions i n the numerical solution of inverse problems\, aiming to face the ill-pose d nature of these problems. In this talk\, we delve into the numerical sol ution of inverse eigenvalue problems from a machine learning perspective\, focusing on the inverse Sturm--Liouville eigenvalue problem for symmetric potentials and the inverse transmission eigenvalue problem for sphericall y symmetric refractive indices. Firstly\, we formulate these eigenvalue pr oblems and pose the numerical solution of the corresponding direct problem s\, using well-known numerical methods. Next\, we present the main ideas b ehind the supervised machine learning regression and briefly discuss the b asic properties of the algorithms we implement\, which are $k$-Nearest Nei ghbours (kNN)\, Random Forests (RF) and Neural Networks (MLP). Afterwards\ , we numerically solve the direct problems and create the spectral data wh ich in turn are used as training data for the machine learning models. We consider examples of inverse problems and compare the performance of each model to predict the unknown potentials and refractive indices respectivel y\, from a given small set of the lowest eigenvalues. Our experiments vali date the efficiency of these machine learning models for numerically solvi ng inverse eigenvalue problems\, providing a proof-of-concept for their ap plicability in this field.\n\n[1] N. Pallikarakis and A. Ntargaras\, Appli cation of machine leraning regression models to inverse eigenvalue problem s\, Computers & Mathematics with Applications\, 154\, 2024.\n LOCATION:https://researchseminars.org/talk/inverseproblems/19/ END:VEVENT END:VCALENDAR