# Constraining Gaussian processes for physics-informed acoustic emission mapping

arXiv: https://arxiv.org/abs/2206.01495 · HTML: https://mlsanity.com/paper/2206.01495/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Gaussian processes with linear operator inequality constraints](https://mlsanity.com/paper/1901.03134/) (2019)
- [Grey-box models for wave loading prediction](https://mlsanity.com/paper/2105.13813/) (2021)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features](https://mlsanity.com/paper/1904.05207/) (2019)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [A Bayesian methodology for localising acoustic emission sources in complex structures](https://mlsanity.com/paper/2012.11058/) (2020)

## Built on by (most cited first, 7 of 7)

- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [On the hierarchical Bayesian modelling of frequency response functions](https://mlsanity.com/paper/2307.06263/) (2023)
- [On the Integration of Physics-Based Machine Learning with Hierarchical Bayesian Modeling Techniques](https://mlsanity.com/paper/2303.00187/) (2023)
- [Meta-models for transfer learning in source localisation](https://mlsanity.com/paper/2305.08657/) (2023)
- [Towards Multilevel Modelling of Train Passing Events on the Staffordshire Bridge](https://mlsanity.com/paper/2403.17820/) (2024)
- [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)

The automated localisation of damage in structures is a challenging but critical ingredient in the path towards predictive or condition-based maintenance of high value structures. The use of acoustic emission time of arrival mapping is a promising approach to this challenge, but is severely hindered by the need to collect a dense set of artificial acoustic emission measurements across the structure, resulting in a lengthy and often impractical data acquisition process. In this paper, we consider the use of physics-informed Gaussian processes for learning these maps to alleviate this problem. In the approach, the Gaussian process is constrained to the physical domain such that information relating to the geometry and boundary conditions of the structure are embedded directly into the learning process, returning a model that guarantees that any predictions made satisfy physically-consistent behaviour at the boundary. A number of scenarios that arise when training measurement acquisition is limited, including where training data are sparse, and also of limited coverage over the structure of interest. Using a complex plate-like structure as an experimental case study, we show that our approach significantly reduces the burden of data collection, where it is seen that incorporation of boundary condition knowledge significantly improves predictive accuracy as training observations are reduced, particularly when training measurements are not available across all parts of the structure.