# Conditional variational autoencoder with Gaussian process regression recognition for parametric models

arXiv: https://arxiv.org/abs/2305.09625 · HTML: https://mlsanity.com/paper/2305.09625/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 16 May 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks](https://mlsanity.com/paper/1904.01514/) (2019)
- [Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation](https://mlsanity.com/paper/2007.12167/) (2020)
- [Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion](https://mlsanity.com/paper/1807.04302/) (2018)

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

- [Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows](https://mlsanity.com/paper/2401.10620/) (2024)

## Abstract (arXiv)

In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the offline stage. However, GPR-based ROM does not perform well for complex systems since POD projection are naturally linear. Conditional variational autoencoder (CVAE) can address this issue via nonlinear neural networks but it has more model complexity, which poses challenges for training and tuning hyperparameters. To this end, we propose a framework of CVAE with Gaussian process regression recognition (CVAE-GPRR). The proposed method consists of a recognition model and a likelihood model. In the recognition model, we first extract low-dimensional features from data by POD to filter the redundant information with high frequency. And then a non-parametric model GPR is used to learn the map from parameters to POD latent variables, which can also alleviate the impact of noise. CVAE-GPRR can achieve the similar accuracy to CVAE but with fewer parameters. In the likelihood model, neural networks are used to reconstruct data. Besides the samples of POD latent variables and input parameters, physical variables are also added as the inputs to make predictions in the whole physical space. This can not be achieved by either GPR-based ROM or CVAE. Moreover, the numerical results show that CVAE-GPRR may alleviate the overfitting issue in CVAE.