PySINDy

Sparse regression over a supplied candidate library, solved in one pass.

algorithm

pysindy

score

NMSE min

cost

light

derivatives

finite_diff

equation form

EVOLUTION

data layout

grid

Usage

import kd

dataset = kd.load_burgers()
model = kd.Model(algorithm="pysindy")
model.fit(dataset)
print(model.best_expr_)

Main parameters

Parameter	Default	Resume	Description
`threshold`	`0.1`	init-only	STLSQ sparsity threshold.
`max_iter`	`20`	init-only	Maximum STLSQ iterations.
`normalize_columns`	`False`	init-only	Normalize library columns before STLSQ.

All fields of PySINDyConfig

Field	Type	Default
`terms`	`tuple[str, ...]`	`('u', 'u_x', 'u_xx', 'mul(u, u_x)')`
`threshold`	`float`	`0.1`
`max_iter`	`int`	`20`
`normalize_columns`	`bool`	`False`
`unbias`	`bool`	`True`
`seed`	`int`	`0`
`extra_optimizer_kwargs`	`dict[str, Any] \\| None`	`None`

The KD wrapper

PySINDy is a third-party package, installed separately, and its authors document the method itself. The points below are specific to driving it from KD.

It runs once. One sparse-regression solve answers the whole run, so a KD run has a single iteration rather than a search curve across generations.

KD supplies the derivatives and the library; PySINDy supplies the solve. PySINDyConfig.terms is the set of candidate term columns, written in KD's function-call notation, and the sequentially thresholded least squares over them is PySINDy's own.

The coefficients are PySINDy's own. Its full coefficient vector is kept in the result, so best_expr_ prints the coefficients the solve produced, without an intervening refit. best_score_ follows from the same coefficients: it is their NMSE on the data of that run, where lower is better.

Anything else the optimizer accepts goes through extra_optimizer_kwargs, unchanged.

References

de Silva et al. (2020). "PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data". J. Open Source Softw. 5(49), 2104. Paper

Kaptanoglu et al. (2022). "PySINDy: A comprehensive Python package for robust sparse system identification". J. Open Source Softw. 7(69), 3994. Paper

Documentation: pysindy.readthedocs.io/en/latest

Code: dynamicslab/pysindy