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Diffrax in a nutshell¤

Diffrax is a JAX-based library providing 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 diffrax

Requires Python >=3.7 and JAX >=0.3.4.

Quick example¤

from diffrax import diffeqsolve, ODETerm, Dopri5
import jax.numpy as jnp

def f(t, y, args):
    return -y

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

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

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},
}

(Also consider starring the project on GitHub!)

Getting started¤

If this page has caught your interest, then have a look at the Getting Started page.

Help

Both Diffrax and its documentation are very new! If:

  • anything is unclear;
  • you have any suggestions;
  • you need any more features;

then please open an issue or pull request on GitHub.