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

arXiv: https://arxiv.org/abs/2201.07753 · HTML: https://mlsanity.com/paper/2201.07753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems](https://mlsanity.com/paper/1901.04878/) (2019)
- [Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates](https://mlsanity.com/paper/2010.05698/) (2020)
- [A deep learning based surrogate model for stochastic simulators](https://mlsanity.com/paper/2110.13809/) (2021)
- [Surrogate assisted active subspace and active subspace assisted surrogate -- A new paradigm for high dimensional structural reliability analysis](https://mlsanity.com/paper/2105.04979/) (2021)
- [Gated Linear Model induced U-net for surrogate modeling and uncertainty quantification](https://mlsanity.com/paper/2111.05123/) (2021)

## Built on by (most cited first, 2 of 2)

- [Multi-fidelity wavelet neural operator with application to uncertainty quantification](https://mlsanity.com/paper/2208.05606/) (2022)
- [CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis](https://mlsanity.com/paper/2603.21678/) (2026)

## Abstract (arXiv)

We propose a novel textitcapsule 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.