TY - JOUR
T1 - Neural-network learning of SPOD latent dynamics
AU - Lario, Andrea
AU - Maulik, Romit
AU - Schmidt, Oliver T.
AU - Rozza, Gianluigi
AU - Mengaldo, Gianmarco
N1 - Funding Information:
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Gianluigi Rozza reports financial support was provided by European Research Council .
Funding Information:
This work was partially supported by MIUR (Italian ministry for university and research) through FARE-X-AROMA-CFD project, P.I. Prof. Gianluigi Rozza. Gianmarco Mengaldo acknowledges support from NUS startup grant R-265-000-A36-133 . This material is partially based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357 . Prof. Gianluigi Rozza acknowledges the support by European Union Funding for Research and Innovation – Horizon 2020 Program – in the framework of European Research Council Executive Agency: Consolidator Grant H2020 ERC CoG 2015 AROMA-CFD project 681447 “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics”.
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower-dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.
AB - We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower-dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.
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U2 - 10.1016/j.jcp.2022.111475
DO - 10.1016/j.jcp.2022.111475
M3 - Article
AN - SCOPUS:85135124563
SN - 0021-9991
VL - 468
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 111475
ER -