Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantification

TL;DR

This paper introduces a capsule network-based encoder-decoder model for surrogate modeling and uncertainty quantification in mechanics, effectively handling high-dimensional sparse data and arbitrary diffusion fields.

Contribution

It adapts Capsule Network architecture for image-to-image regression in surrogate modeling, capturing pose information better than traditional CNNs, and demonstrates its effectiveness on complex SPDE problems.

Findings

Accurate and robust performance on elliptic SPDEs

Efficient handling of high-dimensional sparse data

Flexible response prediction for arbitrary diffusion fields

Abstract

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into image-to-image regression encoder-decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) $-$ retaining pose and position information related to an entity to name a few. The performance of proposed approach is illustrated by solving an elliptic stochastic partial differential equation (SPDE), which also governs systems in mechanics such as steady heat conduction, ground water flow or other diffusion processes, based uncertainty quantification problem with an input dimensionality of $1024$. However, the problem definition does not the restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. The obtained results from performance evaluation indicate that the proposed approach is accurate, efficient, and robust.