# Variational Bayesian surrogate modelling with application to robust design optimisation

arXiv: https://arxiv.org/abs/2404.14857 · HTML: https://mlsanity.com/paper/2404.14857/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 78 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems](https://mlsanity.com/paper/2205.08304/) (2022)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [A probabilistic generative model for semi-supervised training of coarse-grained surrogates and enforcing physical constraints through virtual observables](https://mlsanity.com/paper/2006.01789/) (2020)
- [Fully probabilistic deep models for forward and inverse problems in parametric PDEs](https://mlsanity.com/paper/2208.04856/) (2022)
- [High-Dimensional Bayesian Optimization via Nested Riemannian Manifolds](https://mlsanity.com/paper/2010.10904/) (2020)
- [GP+: A Python Library for Kernel-based learning via Gaussian Processes](https://mlsanity.com/paper/2312.07694/) (2023)
- [Modeling and Optimization with Gaussian Processes in Reduced Eigenbases -- Extended Version](https://mlsanity.com/paper/1908.11272/) (2019)
- [Bayesian model and dimension reduction for uncertainty propagation: applications in random media](https://mlsanity.com/paper/1711.02475/) (2017)
- [Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes](https://mlsanity.com/paper/2008.02386/) (2020)
- [Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis](https://mlsanity.com/paper/2305.13879/) (2023)

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

- [Multi-view Bayesian optimisation in an input-output reduced space for engineering design](https://mlsanity.com/paper/2501.01552/) (2025)

## Abstract (arXiv)

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually high-dimensional and uncertain. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and intrinsic dimensionality reduction. The surrogate is trained by fitting to data obtained from a deterministic computational model. The assumed prior probability density of the surrogate is a Gaussian process. We determine the respective posterior probability density and parameters of the posited statistical model using variational Bayes. The non-Gaussian posterior is approximated by a Gaussian trial density with free variational parameters and the discrepancy between them is measured using the Kullback-Leibler (KL) divergence. We employ the stochastic gradient method to compute the variational parameters and other statistical model parameters by minimising the KL divergence. We demonstrate the accuracy and versatility of the proposed reduced dimension variational Gaussian process (RDVGP) surrogate on illustrative and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.