tinydiffeq

Tiny differentiable ODE/SDE solvers for JAX: fixed-step Euler/RK4, adaptive Tsit5 with an integral step-size controller, and Euler–Maruyama for Itô SDEs. One bounded lax.scan of exactly max_steps iterations serves fixed and adaptive stepping, so shapes are static, nothing recompiles as tolerances or curvature change, and every solve is differentiable in both forward and reverse mode — including reverse-over-forward, the pattern a Levenberg–Marquardt optimizer with geodesic acceleration needs when it differentiates through a rollout.

This is a deliberately small, jvp/vjp-friendly subset of diffrax. Use diffrax if you need pytree states, stiff/implicit solvers, PID control, events, dense output, or checkpointed/backsolve adjoints. tinydiffeq's single runtime dependency is jax.

Install

uv add tinydiffeq

For GPU use, install the JAX accelerator build that matches your hardware, for example:

uv add tinydiffeq "jax[cuda13]"

Minimal example

The vector field may take (x), (x, t), (x, t, args), or (x, t, args, p) — always in that order. args is pass-through data (not an AD target by convention); p holds differentiable parameters (any pytree).

import jax
import jax.numpy as jnp
from tinydiffeq import solve_ode, Tsit5, IController, SaveAt

jax.config.update("jax_enable_x64", True)  # your call — the library never sets it


def f(x, t, args, p):
    return -p * x


sol = solve_ode(
    f, Tsit5(), 0.0, 2.0, jnp.asarray(1.0),
    p=jnp.asarray(1.3),
    dt0=0.1,
    controller=IController(rtol=1e-8, atol=1e-10),
    max_steps=512,
    saveat=SaveAt(ts=jnp.linspace(0.0, 2.0, 21)),  # fixed output shape,
)                                                  # however many steps adapt
print(sol.xs)   # states on the grid
print(sol.ok)   # reached t1 within the max_steps budget?

Gradients through the solve

def endpoint(p):
    return solve_ode(
        f, Tsit5(), 0.0, 2.0, jnp.asarray(1.0), p=p,
        dt0=0.1, controller=IController(rtol=1e-10, atol=1e-12),
        max_steps=512,
    ).xs

jax.grad(endpoint)(jnp.asarray(1.3))                      # reverse mode
jax.jvp(endpoint, (jnp.asarray(1.3),), (jnp.asarray(1.0),))  # forward mode
jax.grad(lambda p: jax.jvp(endpoint, (p,), (jnp.asarray(1.0),))[1])(
    jnp.asarray(1.3)
)                                                          # reverse-over-forward

The step-size controller is wrapped in stop_gradient (accept/reject is non-differentiable either way, and the error-ratio power blows up at exactly zero error); the states differentiate fully through the RK stages. See the docs for the design contracts: static shapes and SaveAt, AD through adaptive stepping, SDE key semantics, and migration recipes from hand-rolled RK4/Tsit5 loops.

License

MIT