PMA Publisher: Published from the Principia Machina source

2026-10-15T19:34:09Z

Published from the Principia Machina source

← Older revision		Revision as of 19:34, 15 October 2026
Line 1:		Line 1:
			{{DISPLAYTITLE:PySINDy}}
	'''PySINDy: Sparse Identification of Equations from Data, Without an Action'''		'''PySINDy: Sparse Identification of Equations from Data, Without an Action'''
	[[Category:Principia Machina]] [[Category:Tools]]		[[Category:Principia Machina]] [[Category:Tools]]
Line 31:		Line 32:
	* '''[[The Principia Machina/Research Toolkit/Bibliography#SINDY16\|SINDY16]]''' – Brunton, S. L., Proctor, J. L., Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS 113, 3932–3937. [https://doi.org/10.1073/pnas.1517384113 doi:10.1073/pnas.1517384113].		* '''[[The Principia Machina/Research Toolkit/Bibliography#SINDY16\|SINDY16]]''' – Brunton, S. L., Proctor, J. L., Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS 113, 3932–3937. [https://doi.org/10.1073/pnas.1517384113 doi:10.1073/pnas.1517384113].
	* '''[[The Principia Machina/Research Toolkit/Bibliography#PDEFIND2017\|PDEFIND2017]]''' – Rudy S.H., Brunton S.L., Proctor J.L., Kutz J.N. (2017). Data-driven discovery of partial differential equations. Science Advances 3(4), e1602614. [https://doi.org/10.1126/sciadv.1602614 doi:10.1126/sciadv.1602614].		* '''[[The Principia Machina/Research Toolkit/Bibliography#PDEFIND2017\|PDEFIND2017]]''' – Rudy S.H., Brunton S.L., Proctor J.L., Kutz J.N. (2017). Data-driven discovery of partial differential equations. Science Advances 3(4), e1602614. [https://doi.org/10.1126/sciadv.1602614 doi:10.1126/sciadv.1602614].

BFP Rauch: 1 revision imported

2026-10-06T03:41:02Z

1 revision imported

← Older revision	Revision as of 03:41, 6 October 2026
(No difference)

DeltaS Zero: Physics tool added 2026-10-06: PySINDy; scores by the research pass, with references (tpm_toolkit 0.1.0)

2026-10-06T03:40:47Z

Physics tool added 2026-10-06: PySINDy; scores by the research pass, with references (tpm_toolkit 0.1.0)

New page

'''PySINDy: Sparse Identification of Equations from Data, Without an Action'''
[[Category:Principia Machina]] [[Category:Tools]]

''Added to the survey on 2026-10-06 by the [[The Principia Machina/Research Toolkit|Research Toolkit]]'s research pass. The scores below are that pass's assessment from the evidence cited under References, on the survey's four axes and scale; they are not the original survey's (2026-09-26), and no rule of the Principia Machina reads them. See [[The Principia Machina/Tools#The additions of 2026-10-06|the additions]] on the front page.''

== Overview & Architectural Fit ==
'''PySINDy''' identifies differential equations from data by sparse regression over a library of candidate functions: it seeks the fewest terms that reproduce the measured time derivatives, <math>\dot{X} \approx \Theta(X)\,\Xi</math> with <math>\Xi</math> sparse. Variants handle partial differential equations (PDE-FIND) and noisy data (weak forms). It is written in Python in the style of scikit-learn.

== Mathematical Evaluation for TPM ==
* '''Lagrangian / Action (3/10):''' Finds equations of motion, not actions; variational structure has to be imposed through custom libraries.
* '''Field / PDE (6.5/10):''' PDE-FIND and weak-form libraries identify partial differential equations from data in space and time.
* '''Relativity (1/10):''' Nothing specific to relativity.
* '''Quantum / Data (8/10):''' Learning from data is the core.

== Integration Pipeline ==
# '''Identify''' equations from the data with no action assumed.
# '''Ask whether they admit a Lagrangian''': test them against the Helmholtz conditions of the inverse problem of the calculus of variations, or compare them with the Euler-Lagrange equations of a Lagrangian found by [[The Principia Machina/Tools/LagrangianNN|a Lagrangian network]] or [[The Principia Machina/Tools/PySR|PySR]].
# '''Read agreement as support''' for the action hypothesis, and disagreement as a pointer to dissipation, a missing variable or a biased library.

== Status, Licence and Limits ==
* '''Status:''' Active. Version 2.1.0 on 8 January 2026 (PyPI), 2.0.0 on 22 August 2025.
* '''Licence:''' MIT.
* '''Home:''' https://github.com/dynamicslab/pysindy
* '''Limits:''' Results depend heavily on the candidate library and on how derivatives are estimated from noisy data. A sparse model is not necessarily the true one.

== On the Principia Machina ==
A tool runs only where the sponsor installed and bound it, and what it returns is untrusted input, vetted before use; its numbers are never values of the site's calculator, TPC. A law it finds is not a register record: it can enter only as the kernel of a new container, and the data it was fitted to can never be the outside value of that law's verification. See [[The Principia Machina/Agent/Tools|Agent/Tools]] and [[The Principia Machina/Tools/Operator's guide|the operator's guide]].

== References ==
* '''[[The Principia Machina/Research Toolkit/Bibliography#PYSINDY2022|PYSINDY2022]]''' – Kaptanoglu A., de Silva B., Fasel U., Kaheman K., Goldschmidt A., Callaham J., Delahunt C., Nicolaou Z., Champion K., Loiseau J.-C., Kutz J., Brunton S. (2022). PySINDy: A comprehensive Python package for robust sparse system identification. JOSS 7(69), 3994. [https://doi.org/10.21105/joss.03994 doi:10.21105/joss.03994].
* '''[[The Principia Machina/Research Toolkit/Bibliography#SINDY16|SINDY16]]''' – Brunton, S. L., Proctor, J. L., Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS 113, 3932–3937. [https://doi.org/10.1073/pnas.1517384113 doi:10.1073/pnas.1517384113].
* '''[[The Principia Machina/Research Toolkit/Bibliography#PDEFIND2017|PDEFIND2017]]''' – Rudy S.H., Brunton S.L., Proctor J.L., Kutz J.N. (2017). Data-driven discovery of partial differential equations. Science Advances 3(4), e1602614. [https://doi.org/10.1126/sciadv.1602614 doi:10.1126/sciadv.1602614].

The Principia Machina/Tools/PySINDy - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: Physics tool added 2026-10-06: PySINDy; scores by the research pass, with references (tpm_toolkit 0.1.0)