# Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery

arXiv: https://arxiv.org/abs/2302.00755 · HTML: https://mlsanity.com/paper/2302.00755/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 68 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 16 of 16)

- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [A toolkit for data-driven discovery of governing equations in high-noise regimes](https://mlsanity.com/paper/2111.04870/) (2021)
- [Bayesian cumulative shrinkage for infinite factorizations](https://mlsanity.com/paper/1902.04349/) (2019)
- [BdryGP: a new Gaussian process model for incorporating boundary information](https://mlsanity.com/paper/1908.08868/) (2019)
- [Graph Based Gaussian Processes on Restricted Domains](https://mlsanity.com/paper/2010.07242/) (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)
- [Convex Modeling of Interactions with Strong Heredity](https://mlsanity.com/paper/1410.3517/) (2014)
- [A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions](https://mlsanity.com/paper/2108.00306/) (2021)
- [Bayesian Factor Analysis for Inference on Interactions](https://mlsanity.com/paper/1904.11603/) (2019)
- [Analysis-of-marginal-Tail-Means (ATM): a robust method for discrete black-box optimization](https://mlsanity.com/paper/1712.03589/) (2017)
- [cmenet: a new method for bi-level variable selection of conditional main effects](https://mlsanity.com/paper/1701.05547/) (2017)

## Built on by (most cited first, 3 of 3)

- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting](https://mlsanity.com/paper/2507.03855/) (2025)
- [Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators](https://mlsanity.com/paper/2410.12690/) (2024)

## Abstract (arXiv)

In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations can often be computationally expensive, and an emulator can be trained to efficiently predict the desired response surface. A widely-used emulator is the Gaussian process (GP), which provides a flexible framework for efficient prediction and uncertainty quantification. Standard GPs, however, do not capture structured sparsity on the underlying response surface, which is present in many applications, particularly in the physical sciences. We thus propose a new hierarchical shrinkage GP (HierGP), which incorporates such structure via cumulative shrinkage priors within a GP framework. We show that the HierGP implicitly embeds the well-known principles of effect sparsity, heredity and hierarchy for analysis of experiments, which allows our model to identify structured sparse features from the response surface with limited data. We propose efficient posterior sampling algorithms for model training and prediction, and prove desirable consistency properties for the HierGP. Finally, we demonstrate the improved performance of HierGP over existing models, in a suite of numerical experiments and an application to dynamical system recovery.