"PARAMETRIC MODEL REDUCTION with CONVOLUTIONAL NEURAL NETWORKS" by Yumeng Wang, Shiping Zhou et al.
 

PARAMETRIC MODEL REDUCTION with CONVOLUTIONAL NEURAL NETWORKS

Abstract

Reduced order modeling (ROM) has been widely used to solve parametric PDEs. However, most existing ROM methods rely on linear projections, which face efficiency challenges when dealing with complex nonlinear problems. In this paper, we propose a convolutional neural network-based ROM method to solve parametric PDEs. Our approach consists of two components: a convolutional autoencoder (CAE) that learns a low-dimensional representation of the solutions, and a convolutional neural network (CNN) that maps the model parameters to the latent representation. For time-dependent problems, we incorporate time t into the surrogate model by treating it as an additional parameter. To reduce computational costs, we use a decoupled training strategy to train the CAE and latent CNN separately. The advantages of our method are that it does not require training data to be sampled at uniform time steps and can predict the solution at any time t within the time domain. Extensive numerical experiments have shown that our surrogate model can accurately predict solutions for both time-independent and time-dependent problems. Comparison with traditional numerical methods further demonstrates the computational effectiveness of our surrogate solver, especially for solving nonlinear parametric PDEs.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS–1953177

Keywords and Phrases

convolutional autoencoder; convolutional neural network; decoupled training strategy; Parametric PDEs; reduced order modeling

International Standard Serial Number (ISSN)

1705-5105

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Global Science Press, All rights reserved.

Publication Date

01 Jan 2024

Link to Full Text

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