Convolutional autoencoder based reduced order modelling for physics problems

Abstract

Numerical solving a full order model can be computationally and time expensive. For real time control problems, it may be infeasible to solve full order models. Reduced order models can be used in order to reduce the time and computational cost while maintaining a high enough accuracy. In this thesis, it will be researched if a convolutional autoencoder based reduced order model is a feasible reduced order modelling method. Reduced order models will be constructed and applied for three different steady state neutron diffusion problems. Every autoencoder receives full order model solutions at its input. Convolutional layers are employed to process the high dimensional input to lower layers. The encoder will map the input data to the low dimensional latent space. The decoder will subsequently reconstruct the high dimensional input at its output from the low dimensional latent space. The latent space between the encoder and decoder forces the autoencoder to capture all necessary information in the few latent variables in such a way that the decoder can reconstruct the full order solution as good as possible. In order to find the optimal values for the model parameters, the autoencoder is trained on a set of full order solutions via gradient descent. After the training, the decoder can be used separately to map from the latent variables to the full order solutions. By joining the decoder with a regression model from the full order model parameters to the latent variables, one can find the full order solution without having to use a full order model solution method, like the finite element approach. In this thesis, a multivariate polynomial regression model is used for the regression from the full order model parameters to the latent variables. The convolutional autoencoder based reduced order model which incorporates residual blocks and parallel residual blocks in its structure, managed to outperform its proper orthogonal decomposition based counterpart by having an approx. 2.5 smaller mean squared error and a 1.4 times smaller mean absolute error. This shows that the proposed method is feasible in terms of prediction performance. Research should be done on the feasibility in terms of the computational costs and time costs. Additional recommendations are the extension of the proposed method to time dependent problems and the application to problems which are harder to capture with proper orthogonal decomposition based models.