A toolkit for data-driven discovery of governing equations in high-noise regimes

by   Charles B. Delahunt, et al.

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the sparse identification of nonlinear dynamics (SINDy) framework. We offer two primary contributions, both focused on noisy data acquired from a system x' = f(x). First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate x'. These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g. 300 the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1 23 into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on x' = f(x), to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model's accuracy and thus a discovery method's effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the true model, enabling more accurate assessment of a discovered model's accuracy.



There are no comments yet.


page 12

page 21

page 28

page 30

page 31


PySINDy: A comprehensive Python package for robust sparse system identification

Automated data-driven modeling, the process of directly discovering the ...

Weak SINDy: Galerkin-Based Data-Driven Model Selection

We present a weak formulation and discretization of the system discovery...

CINDy: Conditional gradient-based Identification of Non-linear Dynamics – Noise-robust recovery

Governing equations are essential to the study of nonlinear dynamics, of...

Weak SINDy: A Data-Driven Galerkin Method for System Identification

We present a weak formulation and discretization of the system discovery...

Data-driven discovery of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes

We introduce a deep neural network learning scheme to learn the Bäcklund...

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Sparse model identification enables the discovery of nonlinear dynamical...

Evolutionary-Based Sparse Regression for the Experimental Identification of Duffing Oscillator

In this paper, an evolutionary-based sparse regression algorithm is prop...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.