# Gradient-based Active Learning with Gaussian Processes for Global Sensitivity Analysis

arXiv: https://arxiv.org/abs/2601.11790 · HTML: https://mlsanity.com/paper/2601.11790/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes](https://mlsanity.com/paper/2407.09739/) (2024)
- [Block Vecchia Approximation for Scalable and Efficient Gaussian Process Computations](https://mlsanity.com/paper/2410.04477/) (2024)

## Built on by (most cited first, 1 of 1)

- [Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection](https://mlsanity.com/paper/2609.33549/) (2026)

## Abstract (arXiv)

Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce the computational burden, provided that the design of computer experiments is enriched efficiently. In this context, we propose an active learning approach that, for a fixed evaluation budget, targets the most informative regions of the input space to improve sensitivity analysis accuracy. More specifically, our method builds on recent advances in active learning for sensitivity analysis (Sobol' indices and derivative-based global sensitivity measures, DGSM) that exploit derivatives obtained from a Gaussian process (GP) surrogate. By leveraging the joint posterior distribution of the GP gradient, we develop acquisition functions that better account for correlations between partial derivatives and their impact on the response surface, leading to a more comprehensive and robust methodology than existing DGSM-oriented criteria. The proposed approach is first compared to state-of-the-art methods on standard benchmark functions, and is then applied to a real environmental model of pesticide transfers.