Gated Linear Model induced U-net for surrogate modeling and uncertainty quantification

TL;DR

This paper introduces GLU-net, a novel deep learning surrogate model combining U-net and Gated Linear Networks, designed for high-dimensional uncertainty quantification with high data efficiency and built-in uncertainty estimation.

Contribution

The paper presents GLU-net, a less complex, data-efficient deep learning architecture that effectively handles high-dimensional uncertainty propagation and provides uncertainty estimates.

Findings

GLU-net achieves high accuracy in high-dimensional Darcy flow problems.

The model is 44% simpler with fewer parameters than existing methods.

GLU-net performs well with sparse data and high input dimensionality.

Abstract

We propose a novel deep learning based surrogate model for solving high-dimensional uncertainty quantification and uncertainty propagation problems. The proposed deep learning architecture is developed by integrating the well-known U-net architecture with the Gaussian Gated Linear Network (GGLN) and referred to as the Gated Linear Network induced U-net or GLU-net. The proposed GLU-net treats the uncertainty propagation problem as an image to image regression and hence, is extremely data efficient. Additionally, it also provides estimates of the predictive uncertainty. The network architecture of GLU-net is less complex with 44\% fewer parameters than the contemporary works. We illustrate the performance of the proposed GLU-net in solving the Darcy flow problem under uncertainty under the sparse data scenario. We consider the stochastic input dimensionality to be up to 4225. Benchmark results are generated using the vanilla Monte Carlo simulation. We observe the proposed GLU-net to be accurate and extremely efficient even when no information about the structure of the inputs is provided to the network. Case studies are performed by varying the training sample size and stochastic input dimensionality to illustrate the robustness of the proposed approach.