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

Understand

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.