Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics

A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state of a system of interest in a parametric setting. A convolutio...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 372; p. 113379
Main Authors: Xu, Jiayang, Duraisamy, Karthik
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2020
Elsevier BV
Subjects:
Autoencoders
Convolutional neural networks
Data-driven modeling
Machine learning
Mathematical models
Model reduction
Modelling
Neural networks
Nonlinear dynamics
Parameters
Prediction models
Reduced order modeling
Spatial data
Training
Wave propagation
Data-driven modeling
Convolutional neural networks
Autoencoders
Reduced order modeling
Machine learning
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state of a system of interest in a parametric setting. A convolutional autoencoder is used as the top level to encode the high dimensional input data along spatial dimensions into a sequence of latent variables. A temporal convolutional autoencoder (TCAE) serves as the second level, which further encodes the output sequence from the first level along the temporal dimension, and outputs a set of latent variables that encapsulate the spatio-temporal evolution of the dynamics. The use of dilated temporal convolutions grows the receptive field exponentially with network depth, allowing for efficient processing of long temporal sequences typical of scientific computations. A fully-connected network is used as the third level to learn the mapping between these latent variables and the global parameters from training data, and predict them for new parameters. For future state predictions, the second level uses a temporal convolutional network to predict subsequent steps of the output sequence from the top level. Latent variables at the bottom-most level are decoded to obtain the dynamics in physical space at new global parameters and/or at a future time. Predictive capabilities are evaluated on a range of problems involving discontinuities, wave propagation, strong transients, and coherent structures. The sensitivity of the results to different modeling choices is assessed. The results suggest that given adequate data and careful training, effective data-driven predictive models can be constructed. Perspectives are provided on the present approach and its place in the landscape of model reduction. •A data-driven framework is proposed for parametric prediction of spatio-temporal dynamics, leveraging nested neural networks.•Convolutional autoencoders are used in space and time to obtain reduced dimensional nonlinear manifolds.•The framework is evaluated on a range of problems involving discontinuities, wave propagation, strong transients, and coherent structures.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2020.113379