DiffraxU

Unit-aware numerical differential equation solvers in JAX.

Diffrax is a JAX-based library providing unit-aware numerical differential equation solvers.

Features include:

• ODE/SDE/CDE (ordinary/stochastic/controlled) solvers;
• lots of different solvers (including Tsit5, Dopri8, symplectic solvers, implicit solvers);
• vmappable everything (including the region of integration);
• using a PyTree as the state;
• dense solutions;
• multiple adjoint methods for backpropagation;
• support for neural differential equations.

From a technical point of view, the internal structure of the library is pretty cool -- all kinds of equations (ODEs, SDEs, CDEs) are solved in a unified way (rather than being treated separately), producing a small tightly-written library.

Installation

pip install git+https://github.com/chaoming0625/diffrax.git

Requires Python 3.9+, JAX 0.4.13+, and Equinox 0.10.11+.

Quick example

import brainunit as u
from diffrax import diffeqsolve, ODETerm, Dopri5

def f(t, y, args):
    return -y / u.ms

term = ODETerm(f)
solver = Dopri5()
y0 = u.math.array([2., 3.]) * u.mV
solution = diffeqsolve(term, solver, t0=0 * u.ms, t1=1 * u.ms, dt0=0.1 * u.ms, y0=y0)

Here, Dopri5 refers to the Dormand--Prince 5(4) numerical differential equation solver, which is a standard choice for many problems.

More examples for unit-aware numerical integration please see unit-aware examples.

Documentation

Available at https://docs.kidger.site/diffrax.

Citation

If you found this library useful in academic research, please cite: (arXiv link)

@phdthesis{kidger2021on,
    title={{O}n {N}eural {D}ifferential {E}quations},
    author={Patrick Kidger},
    year={2021},
    school={University of Oxford},
}