An Improved Multi-dimensional Uncertainty Quantification Method Based on DNN-DRM

Abstract

Mathematical modeling is a method that uses mathematical methods to solve problems in real life. In the process of modeling, the inherent properties of the parameters and the change of the model design conditions will bring great uncertainty to the simulation results. In this paper, a deep neural network and dimension reduction method (DNN-DRM) is proposed to quantify the impact of parameter uncertainty on simulation results in modeling systems with multi-dimensional uncertainty, and reduce the risk caused by uncertainty. Firstly, the methods for training DNN substitute model and testing the generalization ability of models were investigated. Then the DRM based on DNN was constructed to solve the uncertain parameters in the system. In the experiments, three mathematical models with different types of complexity were modeled. Finally, the performance of the method was evaluated by probability distribution, mean and standard deviation of output values. The results show that compared with Monte Carlo simulation (MCS), the DNN-DRM can efficiently and accurately calculate the multi-dimensional uncertainty problem with a strong interaction, and effectively alleviate the “curse of dimensionality” difficulty, which provides a reference for the analysis of problems encountered in real life.