# Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications

arXiv: https://arxiv.org/abs/2302.08329 · HTML: https://mlsanity.com/paper/2302.08329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 69 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems](https://mlsanity.com/paper/1901.04878/) (2019)
- [Extending classical surrogate modelling to high-dimensions through supervised dimensionality reduction: a data-driven approach](https://mlsanity.com/paper/1812.06309/) (2018)
- [Value of information from vibration-based structural health monitoring extracted via Bayesian model updating](https://mlsanity.com/paper/2103.07382/) (2021)
- [Scalable Training of Inference Networks for Gaussian-Process Models](https://mlsanity.com/paper/1905.10969/) (2019)
- [Enabling Dark Energy Science with Deep Generative Models of Galaxy Images](https://mlsanity.com/paper/1609.05796/) (2016)
- [Data-driven Uncertainty Quantification in Computational Human Head Models](https://mlsanity.com/paper/2110.15553/) (2021)
- [High dimensional inference for the structural health monitoring of lock gates](https://mlsanity.com/paper/1812.05529/) (2018)

## Built on by (most cited first, 1 of 1)

- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)

## Abstract (arXiv)

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring (SHM), models capable of both handling high-dimensional data and quantifying uncertainty are required. In this work, our goal is to propose a conditional deep generative model as a surrogate aimed at such applications and high-dimensional stochastic structural simulations in general. To that end, a conditional variational autoencoder (CVAE) utilizing convolutional neural networks (CNNs) is employed to obtain reconstructions of spatially ordered structural response quantities for structural elements that are subjected to stochastic loading. Two numerical examples, inspired by potential SHM applications, are utilized to demonstrate the performance of the surrogate. The model is able to achieve high reconstruction accuracy compared to the reference Finite Element (FE) solutions, while at the same time successfully encoding the load uncertainty.