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SUMMARY:Learning based multi-scale modeling - Prof Kaushik Bhattacharya\, 
 California Institute of Technology
DTSTART:20210226T160000Z
DTEND:20210226T170000Z
UID:TALK156538@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:The behavior of materials involve physics at multiple length a
 nd time scales: electronic\, atomistic\, domains\, defects etc. The engine
 ering properties that we observe and exploit in application are a sum tota
 l of all these interactions. Multiscale modeling seeks to understand how t
 he physics at the finer scales affect the coarser scales. This can be chal
 lenging for two reasons. First\, it is computationally expensive due to th
 e need to repeatedly solve the finer scale model. Second\, it requires a p
 riori (empirical) knowledge of the aspects of the finer-scale behavior tha
 t affect the coarser scale (order parameters\, state variables\, descripto
 rs\, etc.). This is especially challenging in situations where the behavio
 r depends on time. We regard the solution of the finer-scale model as an i
 nput-output map (possibly between infinite dimensional spaces)\, and intro
 duce a a general framework for the data-driven approximation of such maps.
  The proposed approach is motivated by the recent successes of neural netw
 orks and deep learning\, in combination with ideas from model reduction. T
 his combination results in a neural network approximation that is computat
 ionally inexpensive\, independent of the need for a priori knowledge\, and
  can be used directly in the coarser scale calculations. We demonstrate th
 e ideas with examples drawn from first principles study of defects and cry
 stal plasticity study of inelastic impact. The work draws from collaborati
 ons with the Caltech PDE-ML group and in particular Burigede Liu\, Nikola 
 Kovachki and Ying Shi Teh.
LOCATION:Zoom Meeting ID: 819 1682 8857
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