dynamicslab/pysindy

PySINDy – Sparse Identification of Nonlinear Dynamical Systems

What it is:
A Python library that discovers governing equations of dynamical systems directly from measurement data. It implements the SINDy (Sparse Identification of Nonlinear Dynamics) algorithm and several related sparse‑regression methods.

Why it matters:
The models it produces are interpretable (explicit equations) and often compact, making them useful for prediction, control design, or scientific insight without needing a black‑box neural network.

Key capabilities

• Fit continuous‑time dynamical systems from time‑series snapshots.
• Choose among multiple sparse optimizers (e.g., LASSO, SR3, MIOSR, Bayesian SBR).
• Automatic construction of a library of candidate functions (polynomials, trigonometric terms, etc.).
• Built‑in support for custom feature libraries and custom optimizers via optional extras.
• Export the discovered equations in symbolic form, NumPy functions, or LaTeX.

Typical workflow

1. Collect data – a matrix X of state measurements and a time vector t.
2. Create a model – model = pysindy.SINDy() (optionally specify optimizer, feature library, etc.).
3. Fit – model.fit(X, t=t).
4. Inspect – model.print() or model.coefficients() to see the identified equations.
5. Use – simulate forward, design controllers, or analyse the symbolic model.

Installation

pip install pysindy          # core package
# optional optimizers
pip install pysindy[miosr]   # branch‑and‑bound L0 optimizer
pip install pysindy[cvxpy]    # convex SR3 optimizer
pip install pysindy[sbr]     # Bayesian regression optimizer

Conda users can also install via conda install -c conda-forge pysindy.

Minimal example (identifying a simple linear system)

import numpy as np
import pysindy as ps

# synthetic data for x' = -2x, y' = y
t = np.linspace(0, 1, 100)
x = 3 * np.exp(-2 * t)
y = 0.5 * np.exp(t)
X = np.column_stack([x, y])

model = ps.SINDy()
model.fit(X, t=t, feature_names=["x", "y"])
model.print()

Output:

x' = -2.000 x
y' =  1.000 y

Documentation & help

• Full docs: https://pysindy.readthedocs.io
• Video overview & tutorial playlist on YouTube (links in README).
• Issue tracker for bugs/questions: https://github.com/dynamicslab/pysindy/issues
• Contribution guide for adding features or fixing bugs.

Related tools

• Deeptime – time‑series analysis, Markov models.
• PyDMD – Dynamic Mode Decomposition, an alternative data‑driven modeling approach.
• PySINDyGUI / SEED – graphical front‑ends for the same algorithms.

Who should use it Researchers and engineers who need compact, analytically tractable models of physical, biological, or engineered systems from experimental data, especially when interpretability is a priority over raw predictive power.