Serge Guillas

Deyu Ming, Daniel Williamson, Serge Guillas

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast and analytically tractable manner by naturally utilizing the closed form predictive means and variances of linked GP emulators. We demonstrate the method in a series of synthetic examples and empirical applications, and show that it is a competitive candidate for DGP surrogate inference, combining efficiency that is comparable to doubly stochastic variational inference and uncertainty quantification that is comparable to the fully-Bayesian approach. A $\texttt{Python}$ package $\texttt{dgpsi}$ implementing the method is also produced and available at https://github.com/mingdeyu/DGP.

Murray Cutforth, Yiming Yang, Tiffany Fan et al.

Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian Process (GP) model in the binary simulation output case. This paper introduces Bernoulli Parameter Mutual Information (BPMI), a batch active learning algorithm for multi-fidelity GP classifiers. BPMI circumvents the intractability of calculating mutual information in the probability space by employing a first-order Taylor expansion of the link function. We evaluate BPMI against several baselines on two synthetic test cases and a complex, real-world application involving the simulation of a laser-ignited rocket combustor. In all experiments, BPMI demonstrates superior performance, achieving higher predictive accuracy for a fixed computational budget.

Daniel Giles, James Briant, Cyril J. Morcrette et al.

The under-representation of cloud formation is a long-standing bias associated with climate simulations. Parameterisation schemes are required to capture cloud processes within current climate models but have known biases. We overcome these biases by embedding a Multi-Output Gaussian Process (MOGP) trained on high resolution Unified Model simulations to represent the variability of temperature and specific humidity within a climate model. A trained MOGP model is coupled in-situ with a simplified Atmospheric General Circulation Model named SPEEDY. The temperature and specific humidity profiles of SPEEDY are perturbed at fixed intervals according to the variability predicted from the MOGP. Ten-year predictions are generated for both control and ML-hybrid models. The hybrid model reduces the global precipitation bias by 18\% and over the tropics by 22\%. To further understand the drivers of these improvements, physical quantities of interest are explored, such as the distribution of lifted index values and the alteration of the Hadley cell. The control and hybrid set-ups are also run in a plus 4K sea-surface temperature experiment to explore the effects of the approach on patterns relating to cloud cover and precipitation in a warmed climate setting.