# Sequential adaptive design for emulating costly computer codes

arXiv: https://arxiv.org/abs/2206.12113 · HTML: https://mlsanity.com/paper/2206.12113/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [On Active Learning for Gaussian Process-based Global Sensitivity Analysis](https://mlsanity.com/paper/2308.14220/) (2023)
- [Bayesian Optimization by Kernel Regression and Density-based Exploration](https://mlsanity.com/paper/2502.06178/) (2025)

## Abstract (arXiv)

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.