# Deep convolutional neural networks for uncertainty propagation in random fields

## TL;DR

This paper introduces a hierarchical deep convolutional neural network surrogate model for high-dimensional uncertainty propagation, effectively capturing complex input-output relationships in continuum mechanics problems.

## Contribution

The study presents a novel hierarchical CNN architecture tailored for high-dimensional uncertainty quantification, enhancing efficiency and accuracy over traditional methods.

## Key findings

- The surrogate accurately models diverse I/O mappings.
- It effectively characterizes statistical properties of output fields.
- Numerical results outperform Monte Carlo estimates.

## Abstract

The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to describe the high-dimensional system, where the I/O data is first reduced to more manageable dimensions and then the condensed representation is used for surrogate modeling. In this study, we present a new solution scheme for this type of problems based on a deep learning approach. The proposed surrogate is based on a particular network architecture, i.e. the convolutional neural networks. The surrogate architecture is designed in a hierarchical style containing three different levels of model structures, advancing the efficiency and effectiveness of the model in the aspect of training and deploying. To assess the model performance, we carry out uncertainty quantification in a continuum mechanics benchmark problem. Numerical results suggest the proposed model is capable of directly inferring a wide variety of I/O mapping relationships. Uncertainty analysis results obtained via the proposed surrogate have successfully characterized the statistical properties of the output fields compared to the Monte Carlo estimates.