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 Decaying 2D turbulence	Chemistry Gray-Scott patterns	Biology Boids flocking	Economics Sugarscape
Engineering Nagel-Schreckenberg traffic	Mathematics Julia sets	Computer science Game of Life	Social science Schelling segregation

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

There are two ways to use the library. Select a prebuilt system from the catalog by its name, or build a custom system from the general classes of skcomplex.core.components.

Select a prebuilt system

Every prebuilt system has a description, tags, parameters, and references, so you can browse the catalog from Python.

First, list the fields. Each system belongs to one:

from skcomplex.systems import catalog

fields = {system.field for system in catalog()}

Next, list the systems of a field:

bio_eco_systems = {system.name for system in catalog(field='biology/ecology')}

You can also search every field by tag:

oscillation_systems = [system.name for system in catalog() if 'oscillation' in system.tags]

Finally, read the details of the system you chose:

from skcomplex.systems import describe

entry = describe('lotka_volterra')
entry.description, entry.formalism, entry.parameters, entry.references

Simulate any of them with its tuned settings in one line:

from skcomplex.systems import create_simulation

trajectory = create_simulation('sir').prepare().run().trajectory_
round(float(trajectory.values('I.n').max()))

create_system returns a ready-made system with the arguments you choose, so you can simulate it with settings of your own:

from skcomplex.core.engine.runtime import Simulation
from skcomplex.systems import create_system

system = create_system('lotka_volterra', r=1.5)
trajectory = Simulation(system, dt=0.1).prepare().run(until=50).trajectory_
round(float(trajectory.values('prey.n').max()))

Each run can stream to the Rerun viewer:

lotka_volterra Prey and predators cycle

sir An epidemic rises and fades

wolf_sheep Wolves, sheep and grass on a grid

The catalog lists every system by field and tag, 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 Simulation
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 = Simulation(system, dt=0.05).prepare().run(until=30).trajectory_
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 RealTimeClock paces the run against wall time:

import tempfile
from pathlib import Path

from skcomplex.core.engine.runtime import RealTimeClock
from skcomplex.core.engine.viz import RerunObserver

recording = Path(tempfile.mkdtemp()) / 'predators.rrd'
simulation = Simulation(
    system,
    dt=0.05,
    clock=RealTimeClock(speed=20.0),
    observers=[RerunObserver('predators', save_path=recording)],
).prepare()
float(simulation.run(until=30).trajectory_.times[-1])

A simulation started with start runs in the background, and its parameters can change while it runs:

simulation = Simulation(system, dt=0.05, clock=RealTimeClock(speed=20.0)).prepare().start(until=30)
simulation.update_parameters({'hunt.a': 0.2})
simulation.wait()

Adding a process takes one more interaction, and SymbolicAnalysis 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 SymbolicAnalysis


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),
    ],
)
SymbolicAnalysis().prepare(harvested).run().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, validation names the role, the state, and the fix:

from skcomplex.core.engine.compile import PassCompiler


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')],
)
PassCompiler().prepare(wrong).report_.issues[0].text

The compatibility page lists every element, interaction, law, solver, and backend, 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.