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

TL;DR

This paper introduces a multi-view Bayesian optimisation method that uses probabilistic partial least squares to identify a low-dimensional input-output space, significantly improving convergence in engineering design problems.

Contribution

It proposes a novel probabilistic PLS approach within Bayesian optimisation to better identify low-dimensional latent spaces considering both inputs and outputs.

Findings

PPLS-BO outperforms deterministic PLS-BO and classical Bayesian optimisation.

The method achieves faster convergence to the global minimum.

Probabilistic modelling improves the robustness of the optimisation process.

Abstract

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.