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SUMMARY:Long-time prediction of nonlinear parametrized dynamical systems b
 y deep learning-based ROMs - Andrea Manzoni (Politecnico di Milano)
DTSTART:20211119T143000Z
DTEND:20211119T150000Z
UID:TALK165463@talks.cam.ac.uk
DESCRIPTION:Deep learning-based reduced order models (DL-ROMs) have been r
 ecently proposed to overcome common limitations shared by conventional ROM
 s - built\, e.g.\, through proper orthogonal decomposition (POD) - when ap
 plied to nonlinear time-dependent parametrized PDEs. Although extremely ef
 ficient at testing time\, when evaluating the PDE solution for any new tes
 ting-parameter instance\, DL-ROMs require an expensive training stage. To 
 avoid this latter\, a prior dimensionality reduction through POD\, and a m
 ulti-fidelity pretraining stage\, are introduced\, yielding the POD-DL-ROM
  framework\, which allows to solve time-dependent PDEs even faster than in
  real-time. A further step has led us to introduce LSTM networks instead t
 han convolutional autoencoders\, ultimately obtaining POD-LSTM-ROMs that b
 etter grasp the time evolution of the PDE system\, to enhance predictions 
 for new testing-parameter instances.\nEquipped with LSTMs\, POD-LSTM-ROMs 
 also allow us to perform extrapolation of the PDE solution forward in time
 \, that is\, on a (much) larger time domain than the one used to train the
  ROM\, for unseen values of the input parameters - a task often missed by 
 traditional projection-based ROMs. To this aim\, we train a POD-LSTM-ROM o
 n snapshots acquired on a given time interval\, and then approximate the s
 olution on a much longer time window\, taking advantage of a LSTM architec
 ture in a different form besides the POD-LSTM-ROM introduced before. Build
 ing predictions for future times based on the past\, these coupled archite
 ctures mimic the behavior of common numerical solvers for dynamical system
 s. We assess the performance of the proposed framework on several examples
 \, ranging from low-dimensional\, nonperiodic systems to applications in s
 tructural mechanics dealing with micro electromechanical systems\, obtaini
 ng faster than real-time simulations that are able to preserve a remarkabl
 e accuracy across the entire time domain considered during training.
LOCATION:Seminar Room 1\, Newton Institute
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