Deep Convolutional Architectures for Extrapolative Forecast in
Time-dependent Flow Problems
- URL: http://arxiv.org/abs/2209.09651v1
- Date: Sun, 18 Sep 2022 03:45:56 GMT
- Title: Deep Convolutional Architectures for Extrapolative Forecast in
Time-dependent Flow Problems
- Authors: Pratyush Bhatt, Yash Kumar, Azzeddine Soulaimani
- Abstract summary: Deep learning techniques are employed to model the system dynamics for advection dominated problems.
These models take as input a sequence of high-fidelity vector solutions for consecutive time-steps obtained from the PDEs.
Non-intrusive reduced-order modelling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Physical systems whose dynamics are governed by partial differential
equations (PDEs) find applications in numerous fields, from engineering design
to weather forecasting. The process of obtaining the solution from such PDEs
may be computationally expensive for large-scale and parameterized problems. In
this work, deep learning techniques developed especially for time-series
forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN,
are employed to model the system dynamics for advection dominated problems.
These models take as input a sequence of high-fidelity vector solutions for
consecutive time-steps obtained from the PDEs and forecast the solutions for
the subsequent time-steps using auto-regression; thereby reducing the
computation time and power needed to obtain such high-fidelity solutions. The
models are tested on numerical benchmarks (1D Burgers' equation and Stoker's
dam break problem) to assess the long-term prediction accuracy, even outside
the training domain (extrapolation). Non-intrusive reduced-order modelling
techniques such as deep auto-encoder networks are utilized to compress the
high-fidelity snapshots before feeding them as input to the forecasting models
in order to reduce the complexity and the required computations in the online
and offline stages. Deep ensembles are employed to perform uncertainty
quantification of the forecasting models, which provides information about the
variance of the predictions as a result of the epistemic uncertainties.
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