BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:George Em Karniadakis (Brown University) DTSTART:20211104T170000Z DTEND:20211104T180000Z DTSTAMP:20260423T021049Z UID:MPML/58 DESCRIPTION:Title: Op erator regression via DeepOnet: Theory\, Algorithms and Applications\n by George Em Karniadakis (Brown University) as part of Mathematics\, Physi cs and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nWe will review physi cs-informed neural network and summarize available theoretical results. We will also introduce new NNs that learn functionals and nonlinear operator s from functions and corresponding responses for system identification. Th e universal approximation theorem of operators is suggestive of the potent ial of NNs in learning from scattered data any continuous operator or comp lex system. We first generalize the theorem to deep neural networks\, and subsequently we apply it to design a new composite NN with small generaliz ation error\, the deep operator network (DeepONet)\, consisting of a NN fo r encoding the discrete input function space (branch net) and another NN f or encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators\, e.g.\, integrals\, L aplace transforms and fractional Laplacians\, as well as implicit operator s that represent deterministic and stochastic differential equations. More generally\, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously.\n LOCATION:https://researchseminars.org/talk/MPML/58/ END:VEVENT END:VCALENDAR