BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:George Em Karniadakis (Brown University and MIT) DTSTART:20201005T130000Z DTEND:20201005T140000Z DTSTAMP:20260423T021147Z UID:SNPDEA/7 DESCRIPTION:Title: F rom PINNs to DeepOnets: Approximating functions\, functionals\, and operat ors using deep neural networks\nby George Em Karniadakis (Brown Univer sity and MIT) as part of "Partial Differential Equations and Applications" Webinar\n\n\nAbstract\nWe will present a new approach to develop a data-d riven\, learning-based framework for predicting outcomes of physical and b iological systems\, governed by PDEs\, and for discovering hidden physics from noisy data. We will introduce a deep learning approach based on neura l networks (NNs) and generative adversarial networks (GANs). We also intro duce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. Unlike other appro aches that rely on big data\, here we “learn” from small data by explo iting the information provided by the physical conservation laws\, which a re used to obtain informative priors or regularize the neural networks. We will also make connections between Gauss Process Regression and NNs and d iscuss the new powerful concept of meta-learning. We will demonstrate the power of PINNs for several inverse problems in fluid mechanics\, solid mec hanics and biomedicine including wake flows\, shock tube problems\, materi al characterization\, brain aneurysms\, etc\, where traditional methods fa il due to lack of boundary and initial conditions or material properties.\ n LOCATION:https://researchseminars.org/talk/SNPDEA/7/ END:VEVENT END:VCALENDAR