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SUMMARY:Elizabeth Qian (MIT)
DTSTART:20200701T195000Z
DTEND:20200701T201500Z
DTSTAMP:20260423T040216Z
UID:SciDL/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SciDL/8/">Li
 ft & Learn: Analyzable\, Generalizable Data-Driven Models for Nonlinear PD
 Es</a>\nby Elizabeth Qian (MIT) as part of Workshop on Scientific-Driven D
 eep Learning (SciDL)\n\n\nAbstract\nWe present Lift & Learn\, a physics-in
 formed method for learning low-dimensional models for nonlinear PDEs. The 
 method exploits knowledge of a system’s governing equations to identify 
 a coordinate transformation in which the system dynamics have quadratic st
 ructure. This transformation is called a lifting map because it often adds
  auxiliary variables to the system state. The lifting map is applied to da
 ta obtained by evaluating a model for the original nonlinear system. This 
 lifted data is projected onto its leading principal components\, and low-d
 imensional linear and quadratic matrix operators are fit to the lifted red
 uced data using a least-squares operator inference procedure. Analysis of 
 our method shows that the Lift & Learn models are able to capture the syst
 em physics in the lifted coordinates at least as accurately as traditional
  intrusive model reduction approaches. This preservation of system physics
  makes the Lift & Learn models robust to changes in inputs. Numerical expe
 riments on the FitzHugh-Nagumo neuron activation model and the compressibl
 e Euler equations demonstrate the generalizability of our model.\n
LOCATION:https://researchseminars.org/talk/SciDL/8/
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