# Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning

arXiv: https://arxiv.org/abs/2508.16434 · HTML: https://mlsanity.com/paper/2508.16434/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 69 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Deep Gaussian Process Emulation using Stochastic Imputation](https://mlsanity.com/paper/2107.01590/) (2021)
- [MOGPTK: The Multi-Output Gaussian Process Toolkit](https://mlsanity.com/paper/2002.03471/) (2020)
- [On Negative Transfer and Structure of Latent Functions in Multi-output Gaussian Processes](https://mlsanity.com/paper/2004.02382/) (2020)
- [Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models](https://mlsanity.com/paper/2311.18146/) (2023)
- [Stacking designs: designing multi-fidelity computer experiments with target predictive accuracy](https://mlsanity.com/paper/2211.00268/) (2022)
- [Active Learning for a Recursive Non-Additive Emulator for Multi-Fidelity Computer Experiments](https://mlsanity.com/paper/2309.11772/) (2023)

## Abstract (arXiv)

Deep Gaussian Processes (DGPs) are powerful surrogate models known for their flexibility and ability to capture complex functions. However, extending them to multi-output settings remains challenging due to the need for efficient dependency modeling. We propose the Deep Intrinsic Coregionalization Multi-Output Gaussian Process (deepICMGP) surrogate for computer simulation experiments involving multiple outputs, which extends the Intrinsic Coregionalization Model (ICM) by introducing hierarchical coregionalization structures across layers. This enables deepICMGP to effectively model nonlinear and structured dependencies between multiple outputs, addressing key limitations of traditional multi-output GPs. We benchmark deepICMGP against state-of-the-art models, demonstrating its competitive performance. Furthermore, we incorporate active learning strategies into deepICMGP to optimize sequential design tasks, enhancing its ability to efficiently select informative input locations for multi-output systems.