Uncertainty quantification of high-dimensional complex systems by multiplicative polynomial dimensional decompositions

2013 ◽  
Vol 94 (3) ◽  
pp. 221-247 ◽  
Author(s):  
Vaibhav Yadav ◽  
Sharif Rahman
Keyword(s):  
Complex Systems ◽  
Uncertainty Quantification ◽  
High Dimensional

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

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.

scholarly journals Practical reliability and uncertainty quantification in complex systems : final report.

2009 ◽  
Author(s):  
Matthew D. Grace ◽  
James T. Ringland ◽  
Youssef M. Marzouk ◽  
Paul T. Boggs ◽  
Rena M. Zurn ◽  
...  
Keyword(s):  
Complex Systems ◽  
Uncertainty Quantification ◽  
Final Report

scholarly journals A Surrogate Model Based on Artificial Neural Network for RF Radiation Modelling with High-Dimensional Data

2020 ◽  
Vol 17 (7) ◽  
pp. 2586 ◽  
Author(s):  
Xi Cheng ◽  
Clément Henry ◽  
Francesco P. Andriulli ◽  
Christian Person ◽  
Joe Wiart
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Uncertainty Quantification ◽  
Network Architecture ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Attractive Alternative ◽  
Neural Network Architecture ◽  
Radiation Modelling ◽  
Artificial Neural

This paper focuses on quantifying the uncertainty in the specific absorption rate values of the brain induced by the uncertain positions of the electroencephalography electrodes placed on the patient’s scalp. To avoid running a large number of simulations, an artificial neural network architecture for uncertainty quantification involving high-dimensional data is proposed in this paper. The proposed method is demonstrated to be an attractive alternative to conventional uncertainty quantification methods because of its considerable advantage in the computational expense and speed.

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