# Deep convolutional neural networks for uncertainty propagation in random fields

arXiv: https://arxiv.org/abs/1907.11198 · HTML: https://mlsanity.com/paper/1907.11198/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Robust DNN Surrogate Models with Uncertainty Quantification via Adversarial Training](https://mlsanity.com/paper/2211.09954/) (2022)

## Abstract (arXiv)

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.