icrn 0.5.1

Indexed Chemical Reaction Networks in a differentiable, tensor-based framework

icrn

Indexed Chemical Reaction Networks in a differentiable, tensor-based framework.

icrn is a JAX library for specifying chemical reaction networks with indexed species and rate constants, and simulating them as either well-mixed ODEs or reaction–diffusion PDEs. Because everything compiles to jax.numpy operations, simulations are JIT-able, batchable with jax.vmap, and differentiable end-to-end with jax.grad — so rate constants and initial conditions can be trained.

interfaces are subject to change.

Highlights

• Indexed reactions: write M[i] + M[j] -> D[i, j] for a dimer system
• Well-mixed and reaction–diffusion in one API (solve_well_mixed, solve_reaction_diffusion).
• Fast reactions for limiting-reagent-style annihilation (FastReaction).
• JAX-native: works under jit, vmap, and grad.
• Optional non-negativity guards (mode="strict" via checkify, or mode="relu").

Installation

pip install icrn

This installs JAX and NumPy as runtime dependencies. The default JAX wheel is CPU-only; for GPU/TPU, install the best JAX for your platform (JAX installation guide).

Quick Start

Well Mixed Exponential Decay

import jax.numpy as jnp
from icrn import many_species, many_rate_constants, MassActionReaction, solve_well_mixed

A = many_species("A")
k = many_rate_constants("k")

rxns = [MassActionReaction(A, 0, k)]  # A -> 0 with rate k

result = solve_well_mixed(
    rxns,
    conc_vals={A: jnp.array(1.0)},
    rate_constant_vals={k: jnp.array(1.0)},
    times=jnp.array([0.0, jnp.log(2), 1.0]),
    dt=0.005,
)
print(result[A])  # ~ [1.0, 0.5, 0.3679]

Indexed Reactions

The thing that makes icrn different: species and rate constants can carry indices, and reactions involving them are compiled to a single tensor contraction.

import jax.numpy as jnp
from icrn import (
    many_species, many_rate_constants, many_index_symbols,
    MassActionReaction, solve_well_mixed,
)

n = 10
M, D = many_species("M, D")
K1, K2 = many_rate_constants("K_1, K_2")
i, j = many_index_symbols("i, j", n)

# Reversible all-vs-all dimerization
rxns = [
    MassActionReaction(M[i] + M[j], D[i, j], K1[i, j]),
    MassActionReaction(D[i, j], M[i] + M[j], K2[i, j]),
]

conc = {M: jnp.ones(n), D: jnp.zeros((n, n))}
rates = {K1: jnp.ones((n, n)) * 0.1, K2: jnp.ones((n, n)) * 0.05}

out = solve_well_mixed(rxns, conc, rates, times=jnp.array([1.0]), dt=1e-3)

Reaction–diffusion

The Gray-Scott system.

from icrn import solve_reaction_diffusion

U, V = many_species("U, V")
F, k = many_rate_constants("F, k")

rxns = [
    MassActionReaction(U + 2 * V, 3 * V, 1),
    MassActionReaction(V, 0, F + k),
    MassActionReaction(0, U, F),
    MassActionReaction(U, 0, F),
]

sim = solve_reaction_diffusion(
    rxns,
    conc_vals={U: U0, V: V0},                       # 2-D fields
    rate_constant_vals={F: jnp.array(0.037), k: jnp.array(0.06)},
    diffusion_constant_vals={U: jnp.array(0.2), V: jnp.array(0.1)},
    times=jnp.array([5e3]),
    dt=1.0,
    spatial_dims=(101, 101),
    dspaces=(1.0, 1.0),
    mode="relu",
)

Differentiable simulation

Because everything is JAX, you can jit, vmap, and grad straight through a solve:

import jax

@jax.jit
def loss(rate_vals):
    out = solve_well_mixed(rxns, conc, {k: rate_vals}, times, dt)
    return jnp.mean((out[A][-1] - target) ** 2)

grad_fn = jax.grad(loss)

Project layout

icrn/
  symbols.py        # symbolic DSL: Species, IndexSymbol, Complex, TensorExpression
  reactions.py      # MassActionReaction, FastReaction
  solver.py         # solve_well_mixed, solve_reaction_diffusion, solve_with_ops
  operator.py       # operator construction for the splitting integrator
  _internal/        # private JAX kernels (mass-action, diffusion, time stepping)
  utils/            # small helpers (dict_utils)
docs/               # MkDocs site (Material + mkdocstrings)
test/               # reference data for end-to-end tests

Contributing: see CONTRIBUTING.md. Release notes: CHANGELOG.md. PyPI releases are continuously deployed: bump icrn/__init__.py __version__ and merge to main to publish (see Developer notes — Publishing to PyPI).

Development

git clone https://github.com/SwissChardLeaf/icrn
cd icrn
pip install -e ".[dev]"

# tests
python -m unittest discover -s icrn -t .

# lint
ruff check .

# docs
pip install -r docs/requirements.txt
mkdocs serve            # live preview at http://127.0.0.1:8000
mkdocs build --strict   # one-shot build into ./site

Status

• Stable-ish: symbolic DSL (Species, IndexSymbol, Complex), MassActionReaction, solve_well_mixed, solve_reaction_diffusion with spectral diffusion.
• Experimental: FastReaction, mode="strict" runtime checks, Strang splitting.
• Planned: dedicated training utilities, convolutional diffusion solver, benchmarks.

Citation

If you use icrn in academic work, please cite the DNA 31 paper:

Inhoo Lee, Salvador Buse, and Erik Winfree. Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 4:1–4:23. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.DNA.31.4

@InProceedings{lee_et_al:LIPIcs.DNA.31.4,
  author    = {Lee, Inhoo and Buse, Salvador and Winfree, Erik},
  title     = {{Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems}},
  booktitle = {31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages     = {4:1--4:23},
  series    = {Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN      = {978-3-95977-399-7},
  ISSN      = {1868-8969},
  year      = {2025},
  volume    = {347},
  editor    = {Schaeffer, Josie and Zhang, Fei},
  publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address   = {Dagstuhl, Germany},
  URL       = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.4},
  URN       = {urn:nbn:de:0030-drops-238534},
  doi       = {10.4230/LIPIcs.DNA.31.4},
  annote    = {Keywords: Differentiable Programming, Chemical Reaction Networks, Reaction-Diffusion Systems}
}