Semi-supervised deep learning for high-dimensional uncertainty quantification

TL;DR

This paper introduces a semi-supervised deep learning framework combining autoencoders, neural networks, and Gaussian processes to efficiently perform high-dimensional uncertainty quantification and reliability analysis.

Contribution

It proposes a novel semi-supervised approach that reduces dimensionality and improves accuracy in high-dimensional uncertainty quantification tasks.

Findings

Effective dimension reduction via autoencoder.

Accurate surrogate modeling with Gaussian processes.

Successful demonstration on a mathematical example.

Abstract

Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.