PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data

Abstract

Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems models in particular have been widely used to study, explain, and predict system behavior in a wide range of application areas, with examples ranging from Newton's laws of classical mechanics to the Michaelis-Menten kinetics for modeling enzyme kinetics. While governing laws and equations were traditionally derived by hand, the current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including Eureqa (Schmidt & Lipson, 2009), sure independence screening and sparsifying operator (Ouyang, Curtarolo, Ahmetcik, Scheffler, & Ghiringhelli, 2018), and the sparse identification of nonlinear dynamics (SINDy) (Brunton, Proctor, & Kutz, 2016). Maximizing the impact of these model discovery methods requires tools to make them widely accessible to scientists across domains and at various levels of mathematical expertise.

Nonlinear Model Predictive Control of a Robotic Soft Esophagus

“…5 (b) to (d)). Model M 1 discovered by applying DTSINDYC [23] to the collected dataset is given below: It was found that model M 1 given by (11), generalize the entire dataset (black dashed-line plots in Fig. 5 (b) to (d)) with a fraction of noisy training data (m = 500 and n = 3), which confirms the robustness of DTSINDYC modeling with low and noisy data availability.…”

Sparse nonlinear models of chaotic electroconvection

“…Of particular note are its uses in identifying Lorenz-like dynamics from a thermosyphon simulation by Loiseau [ 82 ] and to identify a model for a nonlinear magnetohydrodynamic plasma system by Kaptanoglu et al [ 100 ]. It has also been extended to handle more complex modelling scenarios such as partial differential equations [ 101 , 102 ], systems with inputs or control [ 103 ], to enforce physical constraints [ 80 ], to identify models from corrupt or limited data [ 104 , 105 ] and ensembles of initial conditions [ 106 ], and extending the formulation to include integral terms [ 107 , 108 ], tensor representations [ 109 , 110 ], deep autoencoders [ 111 ], and stochastic forcing [ 112 , 113 ]; an open-source software package, PySINDy, has been developed to integrate a number of these innovations [ 114 ]. We will enforce the symmetries observed above as constraints, as in Loiseau and Brunton [ 80 ].…”

From mechanism-based to data-driven approaches in materials science

“…Also contrary to deep learning approaches the discovered equations are interpretable and also it is fairly easy to communicate them to fellow researchers in either publications or personal communication. Extensions to the existing methods is possible, as the developers have made their programs publicly available in a python package (de Silva et al 2020). The disadvantage of this method is, that it is only as clever as the researcher employing it since this person decides which functions enter .…”