# Efficient dynamic modal load reconstruction using physics-informed Gaussian processes based on frequency-sparse Fourier basis functions

arXiv: https://arxiv.org/abs/2503.09418 · HTML: https://mlsanity.com/paper/2503.09418/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 8 of 8)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [A Gaussian process latent force model for joint input-state estimation in linear structural systems](https://mlsanity.com/paper/1904.00093/) (2019)
- [Understanding and Comparing Scalable Gaussian Process Regression for Big Data](https://mlsanity.com/paper/1811.01159/) (2018)
- [Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes](https://mlsanity.com/paper/2309.11875/) (2023)
- [Physics-informed Gaussian process model for Euler-Bernoulli beam elements](https://mlsanity.com/paper/2308.02894/) (2023)
- [A physics-informed machine learning model for reconstruction of dynamic loads](https://mlsanity.com/paper/2308.08571/) (2023)
- [Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theory](https://mlsanity.com/paper/2405.12802/) (2024)

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

- [Aerodynamic force reconstruction using physics-informed Gaussian processes](https://mlsanity.com/paper/2605.22111/) (2026)
- [Modelling non-linear aeroelastic loads in long-span bridges with extreme learning machines](https://mlsanity.com/paper/2609.33274/) (2026)

## Abstract (arXiv)

Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the Lillebaelt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.