Hybrid Autoencoder/Galerkin Approach for Nonlinear Reduced Order Modelling

56 Pages Posted: 28 Oct 2024

See all articles by Nicolas Lepage

Nicolas Lepage

affiliation not provided to SSRN

Samir Beneddine

affiliation not provided to SSRN

Camilla Fiorini

affiliation not provided to SSRN

Iraj Mortazavi

affiliation not provided to SSRN

Denis Sipp

affiliation not provided to SSRN

Nicolas Thome

Sorbonne University

Abstract

This paper presents a novel nonlinear Reduced Order Model (ROM) that combines Proper Orthogonal Decomposition (POD) with deep learning residual error correction. This new model employs deep learning for error correction in both the projection and time integration phases of the ROM. This enables simultaneous correction of errors within the POD subspace (error in the reduced subspace) and outside (truncation error). The present hybrid ROM is trained using an end-to-end neural Ordinary Differential Equations (ODE) framework for increased accuracy and stability. We evaluate its performance using well-studied test cases: the viscous Burgers equation, the cylinder flow at a single Reynolds number (equal to 100) as well as for Reynolds numbers ranging from 60 to 120 (parametric cylinder case). We show that this novel approach outperforms several existing approaches both in terms of accuracy and dimensionality reduction: POD Galerkin ROMs, a purely data-driven approach using only autoencoders, and also state-of-the-art hybrid methods. furthermore, it offers low computational overhead compared to classical POD-based ROMs, making it attractive for complex 2D or 3D systems.

Keywords: Autoencoder, Reduced order model, Neural ODE, Computational Fluid Dynamics, Deep Learning

Suggested Citation

Lepage, Nicolas and Beneddine, Samir and Fiorini, Camilla and Mortazavi, Iraj and Sipp, Denis and Thome, Nicolas, Hybrid Autoencoder/Galerkin Approach for Nonlinear Reduced Order Modelling. Available at SSRN: https://ssrn.com/abstract=5002010 or http://dx.doi.org/10.2139/ssrn.5002010

Nicolas Lepage (Contact Author)

affiliation not provided to SSRN ( email )

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Samir Beneddine

affiliation not provided to SSRN ( email )

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Camilla Fiorini

affiliation not provided to SSRN ( email )

No Address Available

Iraj Mortazavi

affiliation not provided to SSRN ( email )

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Denis Sipp

affiliation not provided to SSRN ( email )

No Address Available

Nicolas Thome

Sorbonne University ( email )

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