scikit-complexity

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Overview

With scikit-complexity, you can describe a system in any field of science with just a few lines of code, and it takes care of the rest: it works out the mathematics, picks a solver unless you choose one, runs the simulation, and can stream it live to the Rerun viewer.

Complex systems are usually modelled in separate tools with separate conventions, often one for each field. Here they all share one small vocabulary, in the spirit of scikit-learn: elements carry state, interactions change it through laws, and systems nest and compose. Learn it once, and every field opens up.

Physics Cooling coffee	Physics Duffing	Physics Mirollo-Strogatz
Chemistry Brusselator	Chemistry Cubic autocatalysis	Chemistry Cyclic cellular automaton
Biology Agent-based SIR	Biology Boolean repressilator	Biology Replicator dynamics
Economics Correlated geometric Brownian motions	Economics Fishery capital	Economics Geometric Brownian motion
Engineering Chua's circuit	Engineering Memristor oscillator	Engineering Tunnel-diode oscillator
Mathematics Finite-time blow-up	Mathematics Random walk on a hypergraph	Mathematics Julia set
Computer science Majority automaton on the Baumslag-Solitar group	Computer science Majority automaton on the free group	Computer science Game of Life
Social science Hegselmann-Krause	Social science Public goods game on a hypergraph	Social science Prisoner's dilemma tournament

A few of the ready-to-run systems, each with a documented example in the gallery.

Features

• Every kind of dynamics, one interface. Differential equations, stochastic processes, jump processes, discrete maps, cellular automata, agents, networks and hypergraphs, fields and PDEs, quantum systems, and systems that learn by gradient descent.
• The form of your system is inferred. Write the laws, and the framework decides whether it is an ODE, an SDE or a jump process, and compiles it for NumPy, Numba, or JAX.
• Symbols when you want them, code when you don't. Laws are Sage symbolic expressions you can inspect and solve exactly, or plain Python functions.
• Watch it run. Stream any simulation to Rerun in real time, and change its parameters while it runs.
• Analysis included. Nearly 50 analyses, from Lyapunov exponents and entropy to network motifs, scaling laws and system identification, plus experiments for parameter sweeps, sensitivity, calibration and basin stability.
• Standing on mature libraries. SciPy, NetworkX, Mesa, LAMMPS, QuTiP, JAX and others do the heavy lifting.
• Add your own parts without changing the library. Its systems use the same public classes you do, so each one doubles as an example for your own.

Installation

scikit-complexity supports Python 3.12, 3.13, and 3.14 on Linux and on macOS 13 or later with Apple silicon, and is available on PyPI. On Python 3.14 the install builds memory-allocator from source, so it needs a C compiler:

pip install scikit-complexity

The installation includes Sage through the passagemath distributions, LAMMPS, Mesa, Numba, JAX, and Rerun. Windows has no passagemath wheels, so on Windows the package runs in WSL.

For development, clone the repository and install the project with PDM:

git clone https://github.com/georgedouzas/scikit-complexity.git
cd scikit-complexity
pdm install

Usage

The library speaks scikit-learn. What you define is an estimator, a class with get_params, set_params, and clone: elements, interactions, and systems. What you do to them is a function: simulate runs a system as cross_validate runs a model, analyses measure the run as sklearn.metrics scores one, and experiments run many as the model selection functions do.

There are two ways in. Select a ready-made system from the catalog, or build a custom system from the general classes of skcomplex.core.components.

Select a ready-made system

Every ready-made system is a class with a field, topics, references, and parameters. You import it from its subfield, the package skcomplex.systems.<field>.<subfield>, and all_systems finds them, as all_estimators does in scikit-learn.

List the systems of a field:

from skcomplex.systems import all_systems

ecology = [name for name, _ in all_systems(field='biology/ecology')]

Search every field by topic, or by the capability tags of a system:

oscillators = [name for name, _ in all_systems(topics='oscillation')]
stochastic = [name for name, _ in all_systems(field='chemistry', tags={'randomness': 'stochastic'})]

Import the class you chose from its subfield and read what it is:

from skcomplex.systems.biology.ecology import LotkaVolterraSystem

LotkaVolterraSystem.topics, LotkaVolterraSystem.references, LotkaVolterraSystem().get_params()

Simulate it with its tuned settings, or with parameters and settings of your own:

from skcomplex.core.engine.runtime import simulate

trajectory = simulate(LotkaVolterraSystem())
fast_prey = simulate(LotkaVolterraSystem(r=1.5), until=50, dt=0.1)
round(float(fast_prey.values('prey.n').max()))

Each run can stream to the Rerun viewer:

The catalog lists every system by field and topic, and the page of each system shows the classes it is built from.

Build a custom system

A custom system needs only the core. An element declares its states, and an interaction declares its roles and returns its laws, where the namespace s holds the symbols of its parameters and of the elements bound to its roles. A predator and prey system takes one element class, the general RateInteraction, and one new interaction:

from typing import Annotated

from skcomplex.core.components.elements import Element
from skcomplex.core.components.interactions import Interaction, RateInteraction
from skcomplex.core.components.laws import RateLaw
from skcomplex.core.components.system import System
from skcomplex.core.engine.runtime import simulate
from skcomplex.core.specs import ParameterSpec, RoleSpec, StateSpec


class PopulationElement(Element):
    def __init__(self, label, visual=None, *, n: Annotated[float, StateSpec()] = 1.0):
        super().__init__(label, visual=visual)
        self.n = n


class PredationInteraction(Interaction):
    def __init__(
        self,
        label,
        *,
        predator: Annotated[str, RoleSpec(states=('n',))],
        prey: Annotated[str, RoleSpec(states=('n',))],
        a: Annotated[float, ParameterSpec()] = 0.4,
        b: Annotated[float, ParameterSpec()] = 0.1,
    ):
        super().__init__(label)
        self.predator = predator
        self.prey = prey
        self.a = a
        self.b = b

    def _get_laws(self, s):
        contacts = s.predator.n * s.prey.n
        return [RateLaw(s.prey.n, -s.a * contacts), RateLaw(s.predator.n, s.b * contacts)]


system = System(
    elements=[PopulationElement('rabbits', n=40), PopulationElement('foxes', n=9)],
    interactions=[
        RateInteraction('growth', target='rabbits', state='n', rate=lambda s: 1.1 * s.target.n * (1 - s.target.n / 1000)),
        PredationInteraction('hunt', predator='foxes', prey='rabbits'),
        RateInteraction('death', target='foxes', state='n', rate=lambda s: -0.4 * s.target.n),
    ],
)
trajectory = simulate(system, until=30, dt=0.05)
round(float(trajectory.values('rabbits.n').max()))

A RerunObserver records the run for the Rerun viewer, and RerunObserver('predators', spawn=True) opens the viewer during the run. A schedule changes a parameter while the system runs, here halving the hunting rate at time 15:

import tempfile
from pathlib import Path

from skcomplex.core.engine.viz import RerunObserver

recording = Path(tempfile.mkdtemp()) / 'predators.rrd'
trajectory = simulate(
    system,
    until=30,
    dt=0.05,
    observers=[RerunObserver('predators', save_path=recording)],
    schedule={'hunt.a': lambda t: 0.4 if t < 15 else 0.2},
)
float(trajectory.times[-1])

Adding a process takes one more interaction, and the analysis symbolic shows the equations of the system:

from sage.all__sagemath_symbolics import oo
from sage.sets.real_set import RealSet

from skcomplex.core.analysis import symbolic


class HarvestInteraction(Interaction):
    def __init__(
        self,
        label,
        *,
        target: Annotated[str, RoleSpec(states=('n',))],
        h: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.1,
    ):
        super().__init__(label)
        self.target = target
        self.h = h

    def _get_laws(self, s):
        return [RateLaw(s.target.n, -s.h * s.target.n)]


harvested = System(
    elements=[PopulationElement('fish', n=500)],
    interactions=[
        RateInteraction('growth', target='fish', state='n', rate=lambda s: 0.5 * s.target.n * (1 - s.target.n / 1000)),
        HarvestInteraction('fishing', target='fish', h=0.1),
    ],
)
symbolic(harvested).equations['fish.n']

Find out which components fit

An interaction states what it needs from each role, and an element states what it carries. Ask them before you build:

hunt = PredationInteraction('hunt', predator='foxes', prey='rabbits')
hunt.get_requirements().roles['prey'].states, list(PopulationElement('rabbits').get_states())

When a role is bound to an element without the state it reads, simulate raises an error that names the role, the state, and the fix:

from skcomplex.core.errors import RoleElementError


class TankElement(Element):
    def __init__(self, label, visual=None, *, level: Annotated[float, StateSpec()] = 1.0):
        super().__init__(label, visual=visual)
        self.level = level


wrong = System(
    elements=[TankElement('tank'), PopulationElement('foxes')],
    interactions=[PredationInteraction('hunt', predator='foxes', prey='tank')],
)
try:
    simulate(wrong, until=1)
except RoleElementError as error:
    message = str(error)
message

The parts pages list every element, interaction, law, solver, and backend with the tags they accept, and the user guide walks through the choices in order.

Spec-driven development

The project's engineering constitution lives in openspec/constitution.md and binds all work. The project uses OpenSpec for spec-driven development, and openspec/config.yaml names the constitution as binding.

lotka_volterra Prey and predators cycle

sir An epidemic rises and fades

wolf_sheep Wolves, sheep and grass on a grid