Optimistix

<h1 align='center'>Optimistix</h1>

Optimistix is a JAX library for nonlinear solvers: root finding, minimisation, fixed points, and least squares.

Features include:

• interoperable solvers: e.g. autoconvert root find problems to least squares problems, then solve using a minimisation algorithm.
• modular optimisers: e.g. use a BFGS quadratic bowl with a dogleg descent path with a trust region update.
• using a PyTree as the state.
• fast compilation and runtimes.
• interoperability with Optax.
• all the benefits of working with JAX: autodiff, autoparallelism, GPU/TPU support etc.

Installation

pip install optimistix

Requires Python 3.11+.

Documentation

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

Quick example

import jax.numpy as jnp
import optimistix as optx

# Let's solve the ODE dy/dt=tanh(y(t)) with the implicit Euler method.
# We need to find y1 s.t. y1 = y0 + tanh(y1)dt.

y0 = jnp.array(1.)
dt = jnp.array(0.1)

def fn(y, args):
    return y0 + jnp.tanh(y) * dt

solver = optx.Newton(rtol=1e-5, atol=1e-5)
sol = optx.fixed_point(fn, solver, y0)
y1 = sol.value  # satisfies y1 == fn(y1)

Citation

If you found this library to be useful in academic work, then please cite: (arXiv link)

@article{optimistix2024,
    title={Optimistix: modular optimisation in JAX and Equinox},
    author={Jason Rader and Terry Lyons and Patrick Kidger},
    journal={arXiv:2402.09983},
    year={2024},
}

See also: other libraries in the JAX ecosystem

Always useful
Equinox: neural networks and everything not already in core JAX!
jaxtyping: type annotations for shape/dtype of arrays.

Deep learning
Optax: first-order gradient (SGD, Adam, ...) optimisers.
Orbax: checkpointing (async/multi-host/multi-device).
Levanter: scalable+reliable training of foundation models (e.g. LLMs).
paramax: parameterizations and constraints for PyTrees.

Scientific computing
Diffrax: numerical differential equation solvers.
Lineax: linear solvers.
BlackJAX: probabilistic+Bayesian sampling.
sympy2jax: SymPy<->JAX conversion; train symbolic expressions via gradient descent.
PySR: symbolic regression. (Non-JAX honourable mention!)

Awesome JAX
Awesome JAX: a longer list of other JAX projects.

Credit

Optimistix was primarily built by Jason Rader (@packquickly): Twitter; GitHub; Website. It is being co-maintained by Johanna Haffner (@johannahaffner): GitHub; Website.