# Multi-view Bayesian optimisation in an input-output reduced space for engineering design

arXiv: https://arxiv.org/abs/2501.01552 · HTML: https://mlsanity.com/paper/2501.01552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 67 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Builds on (most cited first, 20 of 20)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
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- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
- [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)
- [High Dimensional Bayesian Optimization Assisted by Principal Component Analysis](https://mlsanity.com/paper/2007.00925/) (2020)
- [Modeling and Optimization with Gaussian Processes in Reduced Eigenbases -- Extended Version](https://mlsanity.com/paper/1908.11272/) (2019)
- [Uncertainty quantification for computer models with spatial output using calibration-optimal bases](https://mlsanity.com/paper/1801.08184/) (2018)
- [Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes](https://mlsanity.com/paper/2008.02386/) (2020)
- [Probabilistic partial least squares model: Identifiability, estimation and application](https://mlsanity.com/paper/1706.03597/) (2017)
- [Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization](https://mlsanity.com/paper/2207.11451/) (2022)
- [Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions](https://mlsanity.com/paper/1607.06358/) (2016)
- [Topologically robust CAD model generation for structural optimisation](https://mlsanity.com/paper/1906.07631/) (2019)
- [Infill topology and shape optimisation of lattice-skin structures](https://mlsanity.com/paper/2105.04017/) (2021)
- [Shape optimisation with multiresolution subdivision surfaces and immersed finite elements](https://mlsanity.com/paper/1510.02719/) (2015)
- [Variational Bayesian surrogate modelling with application to robust design optimisation](https://mlsanity.com/paper/2404.14857/) (2024)

## Abstract (arXiv)

Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in engineering design problems, which usually have many design variables but typically a low intrinsic dimensionality. Their scalability can be significantly improved by identifying a low-dimensional space of latent variables that serve as inputs to the Gaussian process. In this paper, we introduce a multi-view learning strategy that considers both the input design variables and output data representing the objective or constraint functions, to identify a low-dimensional latent subspace. Adopting a fully probabilistic viewpoint, we use probabilistic partial least squares (PPLS) to learn an orthogonal mapping from the design variables to the latent variables using training data consisting of inputs and outputs of the black-box computational model. The latent variables and posterior probability densities of the PPLS and Gaussian process models are determined sequentially and iteratively, with retraining occurring at each adaptive sampling iteration. We compare the proposed probabilistic partial least squares Bayesian optimisation (PPLS-BO) strategy with its deterministic counterpart, partial least squares Bayesian optimisation (PLS-BO), and classical Bayesian optimisation, demonstrating significant improvements in convergence to the global minimum.