# Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma

arXiv: https://arxiv.org/abs/2306.07299 · HTML: https://mlsanity.com/paper/2306.07299/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 110 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Yes, but Did It Work?: Evaluating Variational Inference](https://mlsanity.com/paper/1802.02538/) (2018)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Randomly Projected Additive Gaussian Processes for Regression](https://mlsanity.com/paper/1912.12834/) (2019)
- [Variable selection for Gaussian processes via sensitivity analysis of the posterior predictive distribution](https://mlsanity.com/paper/1712.08048/) (2017)
- [A hierarchical expected improvement method for Bayesian optimization](https://mlsanity.com/paper/1911.07285/) (2019)
- [BdryGP: a new Gaussian process model for incorporating boundary information](https://mlsanity.com/paper/1908.08868/) (2019)
- [Exploring the Uncertainty Properties of Neural Networks' Implicit Priors in the Infinite-Width Limit](https://mlsanity.com/paper/2010.07355/) (2020)
- [Monotone Function Estimation for Computer Experiments](https://mlsanity.com/paper/1309.3802/) (2013)
- [Function-on-function kriging, with applications to 3D printing of aortic tissues](https://mlsanity.com/paper/1910.01754/) (2019)
- [Bayesian Uncertainty Quantification for Low-Rank Matrix Completion](https://mlsanity.com/paper/2101.01299/) (2021)
- [Variable Selection Consistency of Gaussian Process Regression](https://mlsanity.com/paper/1912.05738/) (2019)
- [A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions](https://mlsanity.com/paper/2108.00306/) (2021)
- [Projection Pursuit Gaussian Process Regression](https://mlsanity.com/paper/2004.00667/) (2020)
- [Dimension Reduction via Gaussian Ridge Functions](https://mlsanity.com/paper/1802.00515/) (2018)
- [Conglomerate Multi-Fidelity Gaussian Process Modeling, with Application to Heavy-Ion Collisions](https://mlsanity.com/paper/2209.13748/) (2022)
- [Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery](https://mlsanity.com/paper/2302.00755/) (2023)
- [A generalized Gaussian process model for computer experiments with binary time series](https://mlsanity.com/paper/1705.02511/) (2017)

## Built on by (most cited first, 6 of 6)

- [Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators](https://mlsanity.com/paper/2410.01196/) (2024)
- [Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression](https://mlsanity.com/paper/2310.14544/) (2023)
- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)
- [Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design](https://mlsanity.com/paper/2508.01834/) (2025)
- [Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators](https://mlsanity.com/paper/2410.12690/) (2024)
- [eRPCA: Robust Principal Component Analysis for Exponential Family Distributions](https://mlsanity.com/paper/2310.19787/) (2023)

## Abstract (arXiv)

The Quark-Gluon Plasma (QGP) is a unique phase of nuclear matter, theorized to have filled the Universe shortly after the Big Bang. A critical challenge in studying the QGP is that, to reconcile experimental observables with theoretical parameters, one requires many simulation runs of a complex physics model over a high-dimensional parameter space. Each run is computationally very expensive, requiring thousands of CPU hours, thus limiting physicists to only several hundred runs. Given limited training data for high-dimensional prediction, existing surrogate models often yield poor predictions with high predictive uncertainties, leading to imprecise scientific findings. To address this, we propose a new Additive Multi-Index Gaussian process (AdMIn-GP) model, which leverages a flexible additive structure on low-dimensional embeddings of the parameter space. This is guided by prior scientific knowledge that the QGP is dominated by multiple distinct physical phenomena (i.e., multiphysics), each involving a small number of latent parameters. The AdMIn-GP models for such embedded structures within a flexible Bayesian nonparametric framework, which facilitates efficient model fitting via a carefully constructed variational inference approach with inducing points. We show the effectiveness of the AdMIn-GP via a suite of numerical experiments and our QGP application, where we demonstrate considerably improved surrogate modeling performance over existing models.