# Physics-informed Gaussian process model for Euler-Bernoulli beam elements

arXiv: https://arxiv.org/abs/2308.02894 · HTML: https://mlsanity.com/paper/2308.02894/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 11 references that are in the map.
- First posted on arXiv 5 Aug 2023.

## Builds on (most cited first, 5 of 5)

- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Approximate Inference for Fully Bayesian Gaussian Process Regression](https://mlsanity.com/paper/1912.13440/) (2019)
- [Differential equations, splines and Gaussian processes](https://mlsanity.com/paper/2102.03306/) (2021)

## Built on by (most cited first, 4 of 4)

- [Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes](https://mlsanity.com/paper/2309.11875/) (2023)
- [A physics-informed machine learning model for reconstruction of dynamic loads](https://mlsanity.com/paper/2308.08571/) (2023)
- [Efficient dynamic modal load reconstruction using physics-informed Gaussian processes based on frequency-sparse Fourier basis functions](https://mlsanity.com/paper/2503.09418/) (2025)
- [Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theory](https://mlsanity.com/paper/2405.12802/) (2024)

## Abstract (arXiv)

A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the structure's bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed model is applied on a numerically simulated cantilever beam, where the regressed bending stiffness is evaluated and the influence measurement noise on the prediction quality is investigated. Further, the regressed probabilistic stiffness distribution is used in a structural health monitoring context, where the Mahalanobis distance is employed to reason about the possible location and extent of damage in the structural system. To validate the developed framework, an experiment is conducted and measured heterogeneous datasets are used to update the assumed analytical structural model.