High-dimensional engineering design optimisation is intractable for classical Bayesian optimisation, which degrades beyond roughly ten design variables. This concept covers a method that learns a low-dimensional latent space shared by BOTH the design inputs and the simulated quantities of interest, using probabilistic partial least squares: a generative latent-variable model s = Wz + noise, y = Qz + noise with orthonormal W and Q, trained by variational Bayes with an alternating expectation-maximisation scheme, where the latent dimension is chosen by monitoring the change in the evidence lower bound. Unlike PCA or random-embedding reductions, which see only the input view, and unlike active-subspace methods, which need gradients of the expensive solver, the multi-view construction lets the response itself decide which directions of design space matter. A Gaussian-process surrogate and acquisition function (upper confidence bound or expected improvement, optionally constrained and maximised with a non-dominated-sorting genetic algorithm) then operate entirely in the latent space, and both the latent posterior and the surrogate are retrained at every iteration so the reduction adapts as evidence accumulates. Demonstrated on finite-element structural design problems, it reaches comparable designs several times faster than optimisation in the full space.
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 processe…