sindy-skill

name

sindy-skill

description

Sparse Identification of Nonlinear Dynamical Systems (SINDy) using PySINDy. Use this skill when the user wants to (1) discover governing equations from time-series data, (2) perform sparse regression on dynamical systems, (3) identify ODEs or PDEs from measurement data, (4) use PySINDy for system identification, (5) build SINDy models with different optimizers or feature libraries, (6) simulate or predict dynamical system behavior from discovered equations. Trigger when user mentions SINDy, PySINDy, sparse identification, system identification from data, equation discovery, data-driven dynamics, or governing equation learning.

SINDy Skill

Discover sparse governing equations (ODEs/PDEs) from time-series data using PySINDy.

Environment Setup

Before using PySINDy, ensure the environment is ready:

bash scripts/setup_env.sh [optional/venv/path]

This creates a venv with pysindy[cvxpy], matplotlib, and scipy. If the user already has pysindy installed, skip this step.

Minimum install (no venv script):

pip install pysindy matplotlib scipy

For advanced optimizers:

pip install "pysindy[cvxpy]"    # SR3, ConstrainedSR3, TrappingSR3, StableLinearSR3, SINDyPI
pip install "pysindy[miosr]"    # MIOSR (requires Gurobi license)
pip install "pysindy[sbr]"      # SBR (JAX + NumPyro)

Quick Start Workflow

SINDy solves: dX/dt = Theta(X) * Xi, where Theta is a feature library and Xi are sparse coefficients.

1. Prepare Data

import numpy as np
import pysindy as ps

# X: shape (n_samples, n_features) - state measurements
# t: shape (n_samples,) - time points

2. Build and Fit Model

model = ps.SINDy(
    differentiation_method=ps.FiniteDifference(order=2),
    feature_library=ps.PolynomialLibrary(degree=3),
    optimizer=ps.STLSQ(threshold=0.1),
)
model.fit(X, t=t, feature_names=["x", "y"])
model.print()

3. Evaluate and Use

score = model.score(X, t=t)         # R^2 score
x_dot = model.predict(X)             # predicted derivatives
x_sim = model.simulate(X[0], t)      # simulate from initial condition
coeffs = model.coefficients()        # sparse coefficient matrix

CLI Tool

For quick analysis from CSV data, run scripts/sindy_analyze.py:

python scripts/sindy_analyze.py data.csv --degree 3 --threshold 0.1 --simulate

The CSV must have a time (or t) column. All other columns are treated as state variables.

Options: --library poly|fourier|poly+fourier, --optimizer stlsq|sr3|ssr|frols, --output equations.txt, --simulate.

Component Selection Guide

Differentiation (compute dX/dt from X)

Data Quality	Method
Clean	FiniteDifference(order=2) (default)
Mild noise	SmoothedFiniteDifference()
Periodic	SpectralDerivative()
Noisy	SINDyDerivative(kind="kalman", alpha=0.05)
Known derivatives	Pass x_dot= to fit() directly

Feature Library (candidate functions Theta)

System Type	Library
General nonlinear	PolynomialLibrary(degree=2-5)
Oscillatory	FourierLibrary(n_frequencies=3)
Mixed	ConcatLibrary([PolynomialLibrary(), FourierLibrary()])
Domain-specific	CustomLibrary(library_functions=[...])
PDEs	PDELibrary(...) or WeakPDELibrary(...)

Optimizer (sparse regression for Xi)

Scenario	Optimizer
Default / simple	STLSQ(threshold=0.1)
Flexible regularization	SR3(threshold=0.1) (needs cvxpy)
Known constraints	ConstrainedSR3(...) (needs cvxpy)
Stability guarantee	TrappingSR3(...) (needs cvxpy)
Fast greedy	SSR() or FROLS()
Exact L0 sparsity	MIOSR(l0_bound=10) (needs gurobipy)
Noisy data	EnsembleOptimizer(opt=STLSQ(), bagging=True, n_models=20)

Common Patterns

Lorenz System Example

from scipy.integrate import solve_ivp
from pysindy.utils.odes import lorenz

sol = solve_ivp(lorenz, (0, 10), [-8, 8, 27],
                t_eval=np.linspace(0, 10, 2000), max_step=0.01)
model = ps.SINDy(optimizer=ps.STLSQ(threshold=0.2))
model.fit(sol.y.T, t=sol.t, feature_names=["x", "y", "z"])
model.print()

Multiple Trajectories

model.fit([X1, X2, X3], t=[t1, t2, t3])

With Control Inputs

model.fit(X, t=t, u=U)  # U shape: (n_samples, n_controls)
model.simulate(x0, t, u=u_func)  # u_func(t) returns control vector

References

• Full API reference (all classes, methods, parameters): See references/api_overview.md
• Advanced patterns (noise handling, PDEs, ensembles, constraints, tuning): See references/advanced_patterns.md