# Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions

arXiv: https://arxiv.org/abs/2510.21974 · HTML: https://mlsanity.com/paper/2510.21974/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1806.05490/) (2018)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Variational Auto-encoded Deep Gaussian Processes](https://mlsanity.com/paper/1511.06455/) (2015)
- [Nonstationary Gaussian Process Surrogates](https://mlsanity.com/paper/2305.19242/) (2023)
- [Approximate Inference for Nonstationary Heteroscedastic Gaussian process Regression](https://mlsanity.com/paper/1404.5443/) (2014)
- [Sequential Adaptive Design for Jump Regression Estimation](https://mlsanity.com/paper/1904.01648/) (2019)
- [Massively parallel approximate Gaussian process regression](https://mlsanity.com/paper/1310.5182/) (2013)

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

- [Online Bayesian Calibration under Gradual and Abrupt System Changes](https://mlsanity.com/paper/2605.06612/) (2026)
- [Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selection](https://mlsanity.com/paper/2609.33550/) (2026)

## Abstract (arXiv)

We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of a piecewise continuous function on a high-dimensional domain. DJGP addresses the limitations of conventional Jump Gaussian Processes (JGP) in high-dimensional input spaces by integrating region-specific, locally linear projections with JGP modeling. These projections employ region-dependent matrices to capture local low-dimensional subspace structures, making them well suited to the inherently localized modeling behavior of JGPs, a variant of local Gaussian processes. To control model complexity, we place a Gaussian Process prior on the projection matrices, allowing them to evolve smoothly across the input space. The projected inputs are then modeled with a JGP to capture piecewise continuous relationships with the response. This yields a distinctive two-layer deep learning of GP/JGP. We further develop a scalable variational inference algorithm to jointly learn the projection matrices and JGP hyperparameters. Rigorous theoretical analysis and extensive empirical studies are provided to justify the proposed approach. In particular, we derive an oracle error bound for DJGP and decompose it into four distinct sources of error, which are then linked to practical implications. Experiments on synthetic and benchmark datasets demonstrate that DJGP achieves superior predictive accuracy and more reliable uncertainty quantification compared with existing methods.