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X-ORIGINAL-URL:https://www.cmm.uchile.cl/
X-WR-CALNAME:CMM
X-WR-CALDESC:Centro de Modelamiento Matemático
X-WR-TIMEZONE:America/Santiago
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TZID:America/Santiago
X-LIC-LOCATION:America/Santiago
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TZOFFSETFROM:-0400
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TZNAME:-04
DTSTART:20260618T034032
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DTSTART;TZID=America/Santiago:20260617T161500
DTEND;TZID=America/Santiago:20260617T180000
DTSTAMP:20260610T152002Z
CREATED:20260610
LAST-MODIFIED:20260610
PRIORITY:5
SEQUENCE:1
TRANSP:OPAQUE
SUMMARY:Optimization and Equilibrium Seminar: Bilevel learning for PDE inverse problems
DESCRIPTION:Abstract: In recent years, the integration of optimization techniques with machine learning paradigms has led to significant advances in solving inverse problems, particularly through the optimal selection of parameters or observation strategies. A rigorous and systematic approach to tackle such problems is provided by bilevel optimization, where the lower-level problem corresponds to a model-based inverse problem—often governed by a partial differential equation (PDE)—and the upper-level objective encodes a data-driven loss functional, typically defined over a training set. Unlike classical variational models, the presence of PDE constraints introduces substantial analytical and computational challenges. In this talk, I will present a bilevel optimization framework for PDE-constrained inverse problems, and discuss recent results on the existence of optimal parameters. Furthermore, I will explore the possibility of reformulating the bilevel problem as a single-level optimization problem under suitable assumptions. Finally, I will derive and discuss first-order optimality conditions for the resulting problem, highlighting key mathematical difficulties and future directions.\nSpeaker: Juan Carlos De Los Reyes (Centro de Modelización Matemática MODEMAT y Escuela Politécnica Nacional, Quito).\nThe link to join the seminar is:\nhttps://uchile.zoom.us/j/98721784149?pwd=df7YyCDGwMXlNuDX0kwKvob08edgk7.1\n
URL:https://www.cmm.uchile.cl/events/optimization-and-equilibrium-seminar-bilevel-learning-for-pde-inverse-problems/
ORGANIZER;CN=CMM:MAILTO:
CATEGORIES:Seminarios
LOCATION:Sala John Von Neumann, 7th floor, Beauchef 851
ATTACH;FMTTYPE=image/jpeg:https://www.cmm.uchile.cl/wp-content/uploads/2026/05/Optimizacion-y-equilibrio.jpg
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