Differentiable particle-based physics for proliferating cells and active matter, built with JAX and Equinox.

• Differentiable end-to-end — pathwise gradients through the continuous physics, score-function gradients through discrete events.
• Composable physics steps — mechanics, diffusion, Brownian and active-Brownian dynamics, growth, division, and death.
• Principled time-stepping — steps compose into one macro-step by Lie-Trotter operator splitting: each advances the shared state over dt, giving a consistent, first-order-accurate integrator of the coupled dynamics.
• Continuous-time dynamics and control — neural-ODE and gene-network controllers that model cell decision making from local cues.
• Core abstractions built for easy extension — add your own physics steps to the pipeline. Guides provided with the library for coding agents reference.
• JAX and Equinox native — jit, vmap, Equinox filtered transformations and neural-network modules work throughout the pipeline; GPU support out of the box.

See Key Concepts and usage guides for more.

jax-morph requires Python 3.11 or later.

pip install jax-morph

Or with uv:

uv add jax-morph

The visualization API is an optional matplotlib-backed extra. Install it when using jxm.viz.draw, jxm.viz.animate, or jxm.viz.plot_timeseries:

pip install 'jax-morph[viz]'

Or with uv:

uv add 'jax-morph[viz]'

The base package does not install matplotlib; import jax_morph.viz remains available, and a rendering call explains how to add the extra if it is missing.

This model seeds a single cell that diffuses under a pairwise interaction and stochastically divides:

import jax

import jax_morph as jxm
from jax_morph.physics import BrownianDynamics, Division, SoftSphere

# Cells diffuses under a soft-sphere interaction and divide stochastically
model = jxm.Model(
    [
        BrownianDynamics(SoftSphere(), n_space_dim=2, kT=0.05),
        Division(n_space_dim=2),
    ]
)

# Build state class and initialize with a single cell
StateClass = jxm.build_state_from_model(model)
state = StateClass.init_empty(capacity=32, n_space_dim=2, n_types=1)
state = state.update(
    alive=state.alive.at[0].set(True),
    radius=state.radius.at[0].set(0.5),
    celltype=state.celltype.at[0, 0].set(1.0),
    division_rate=state.division_rate.at[0].set(1.0),
)

# Simulate
sim_key = jax.random.PRNGKey(0)
final_state = jxm.simulate(model, state, n_steps=20, dt=0.1, key=sim_key)

See the documentation and example notebooks for more.

Usage guides ship with the library so they remain available with a PyPI installation and match the installed API version:

import jax_morph as jxm

jxm.guides.list_guides()
jxm.guides.guide('extending')
jxm.guides.guide('optimization/pathwise')

If you use JAX-Morph, please cite:

@article{deshpandemottes2025,
  title={Engineering morphogenesis of cell clusters with differentiable programming},
  author={Deshpande, Ramya and Mottes, Francesco and Vlad, Ariana-Dalia and Brenner, Michael P and Dal Co, Alma},
  journal   = {Nature Computational Science},
  year      = {2025},
  doi       = {10.1038/s43588-025-00851-4},
  url       = {https://doi.org/10.1038/s43588-025-00851-4}
}

The published paper can be read here.