# Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements

arXiv: https://arxiv.org/abs/2409.20510 · HTML: https://mlsanity.com/paper/2409.20510/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 9 of 9)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Learning Discrepancy Models From Experimental Data](https://mlsanity.com/paper/1909.08574/) (2019)
- [Online Weak-form Sparse Identification of Partial Differential Equations](https://mlsanity.com/paper/2203.03979/) (2022)
- [Simultaneous Identification and Denoising of Dynamical Systems](https://mlsanity.com/paper/2203.13837/) (2022)
- [A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study](https://mlsanity.com/paper/2201.12683/) (2022)
- [Deep learning for full-field ultrasonic characterization](https://mlsanity.com/paper/2301.02378/) (2023)
- [Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data](https://mlsanity.com/paper/2406.02581/) (2024)

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

- [Network scaling and scale-driven loss balancing for intelligent poroelastography](https://mlsanity.com/paper/2411.08886/) (2024)
- [Physics-Informed Neural Networks with Unknown Partial Differential Equations: an Application in Multivariate Time Series](https://mlsanity.com/paper/2503.20144/) (2025)

## Abstract (arXiv)

This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.