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SUMMARY:From Inertial Manifolds to Latent Geometry: Data-Driven Manifolds 
 for Complex Systems - Eleni D. Koronaki (Luxembourg Institute of Science a
 nd Technology)
DTSTART:20251120T150000Z
DTEND:20251120T160000Z
UID:TALK239272@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:This talk discusses how analytical and data-driven perspective
 s jointly contribute to understanding the low-dimensional geometry underly
 ing complex dynamical systems. Building on concepts such as inertial and a
 pproximate inertial manifolds for dissipative equations\, we show how mode
 rn manifold-learning and neural networks can complement classical analysis
  by discovering similar structures directly from data. Techniques includin
 g Diffusion Maps\, autoencoders\, and gray-box corrections yield interpret
 able reduced dynamics that remain faithful to the governing physics. Illus
 trative examples span dissipative partial differential equations\, thin-fi
 lm flows\, and canonical nonlinear oscillators such as the Lorenz and Rös
 sler systems. Extending this geometric view further\, we demonstrate how A
 lternating Diffusion Maps identify shared and system-specific latent varia
 bles across heterogeneous sensors in multi-view settings. Together\, these
  developments highlight a growing synthesis between mathematical analysis 
 and data-driven modeling in revealing the hidden manifolds that organize c
 omplex dynamics.
LOCATION:Centre for Mathematical Sciences\, MR14
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