@Article{IJNAM-21-716,
author = {Wang , YumengZhou , Shiping and Zhang , Yanzhi},
title = {Parametric Model Reduction with Convolutional Neural Networks},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {5},
pages = {716--738},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1029},
url = {http://global-sci.org/intro/article_detail/ijnam/23450.html}
}