# Nonnegativity-Enforced Gaussian Process Regression

arXiv: https://arxiv.org/abs/2004.04632 · HTML: https://mlsanity.com/paper/2004.04632/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Constraining Gaussian processes for physics-informed acoustic emission mapping](https://mlsanity.com/paper/2206.01495/) (2022)
- [Learning thermodynamically constrained equations of state with uncertainty](https://mlsanity.com/paper/2306.17004/) (2023)
- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
- [Monotonic Gaussian process for physics-constrained machine learning with materials science applications](https://mlsanity.com/paper/2209.00628/) (2022)
- [Time-Varying Transition Matrices with Multi-task Gaussian Processes](https://mlsanity.com/paper/2306.11772/) (2023)
- [Gaussian Process Regression with Soft Inequality and Monotonicity Constraints](https://mlsanity.com/paper/2404.02873/) (2024)
- [Respecting the limit:Bayesian optimization with a bound on the optimal value](https://mlsanity.com/paper/2411.04744/) (2024)
- [Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Models](https://mlsanity.com/paper/2601.03367/) (2026)
- [Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression](https://mlsanity.com/paper/2603.19907/) (2026)
- [From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?](https://mlsanity.com/paper/2609.33387/) (2026)

## Abstract (arXiv)

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy model which is unbounded for all temporal or spacial points, and thus leaves the possibility of taking on infeasible values. We propose an approach to enforce the physical constraints in a probabilistic way under the GP regression framework. In addition, this new approach reduces the variance in the resulting GP model.