Sequential adaptive design for emulating costly computer codes

TL;DR

This paper introduces VIGF, a novel adaptive sampling criterion for Gaussian process surrogates, improving the efficiency of emulating costly computer models through sequential and batch strategies, including multi-fidelity extensions.

Contribution

The paper proposes VIGF, a new adaptive sampling method for GPs, with batch and multi-fidelity extensions, outperforming existing strategies in surrogate modeling of expensive simulations.

Findings

VIGF outperforms existing sampling strategies on benchmark functions.

Batch VIGF reduces computational time with parallel processing.

Multi-fidelity VIGF effectively combines low- and high-fidelity models.

Abstract

Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of model evaluations remains challenging. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). The improvement function at any point is a measure of the deviation of the GP emulator from the nearest observed model output. At each iteration of the proposed algorithm, a new run is performed where VIGF is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. A batch version of VIGF is also proposed which can save the user time when parallel computing is available. Additionally, VIGF is extended to the multi-fidelity case where the expensive high-fidelity model is predicted with the assistance of a lower fidelity simulator. This is performed via hierarchical kriging. The applicability of our method is assessed on a bunch of test functions and its performance is compared with several sequential sampling strategies. The results suggest that our method has a superior performance in predicting the benchmark functions in most cases. An implementation of VIGF is available in the dgpsi R package, which can be found on CRAN.