# GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations

arXiv: https://arxiv.org/abs/2405.08613 · HTML: https://mlsanity.com/paper/2405.08613/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 17 of 17)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Data-driven discovery of PDEs in complex datasets](https://mlsanity.com/paper/1808.10788/) (2018)
- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Differentiable Physics-informed Graph Networks](https://mlsanity.com/paper/1902.02950/) (2019)
- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [A Robust SINDy Approach by Combining Neural Networks and an Integral Form](https://mlsanity.com/paper/2309.07193/) (2023)
- [Model discovery in the sparse sampling regime](https://mlsanity.com/paper/2105.00400/) (2021)

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

- [Asynchronous Federated Learning: A Scalable Approach for Decentralized Machine Learning](https://mlsanity.com/paper/2412.17723/) (2024)
- [Parameter-Aware Ensemble SINDy for Interpretable Symbolic SGS Closure](https://mlsanity.com/paper/2508.14085/) (2025)

## Abstract (arXiv)

The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in the discovery of models for nonlinear partial differential equations (PDEs) lies in addressing the challenges posed by the curse of dimensionality and large datasets. Consequently, the strategic selection of the most informative samples within a given dataset plays a crucial role in reducing computational costs and enhancing the effectiveness of SINDy-based algorithms. To this aim, we employ a greedy sampling approach to the snapshot matrix of a PDE to obtain its valuable samples, which are suitable to train a deep neural network (DNN) in a SINDy framework. SINDy based algorithms often consist of a data collection unit, constructing a dictionary of basis functions, computing the time derivative, and solving a sparse identification problem which ends to regularised least squares minimization. In this paper, we extend the results of a SINDy based deep learning model discovery (DeePyMoD) approach by integrating greedy sampling technique in its data collection unit and new sparsity promoting algorithms in the least squares minimization unit. In this regard we introduce the greedy sampling neural network in sparse identification of nonlinear partial differential equations (GN-SINDy) which blends a greedy sampling method, the DNN, and the SINDy algorithm. In the implementation phase, to show the effectiveness of GN-SINDy, we compare its results with DeePyMoD by using a Python package that is prepared for this purpose on numerous PDE discovery