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Probabilistic solvers for differential equations in JAX¤

ProbDiffEq implements adaptive probabilistic numerical solvers for initial value problems.

It inherits automatic differentiation, vectorisation, and GPU capability from JAX. Features include:

  • Stable implementation
  • Calibration, step-size adaptation, and checkpointing
  • State-space model factorisations
  • Dense output and posterior sampling
  • Filtering, smoothing, and many other backends
  • Custom information operators
  • Physics-enhanced regression
  • Compatibility with other JAX-based libraries such as Optax or BlackJAX.

and many more.


Get the most recent stable version from PyPi:

pip install probdiffeq
This installation assumes that JAX is already available.

To install ProbDiffEq with jax[cpu], run

pip install probdiffeq[cpu]

What's next?¤

There are examples and there are advanced examples.

Consult the examples first. They show how to interact with the API, and explain some useful facts about probabilistic numerical solvers.

The advanced examples show applications of probabilistic numerical solvers, often in conjunction with external libraries. For example, this notebook shows how to combine ProbDiffEq with Optax, and this notebook does the same with BlackJAX.

Proceed with the quickstart and the examples before moving to the advanced examples and the API documentation.


Contributions are absolutely welcome! Start with checking the existing issues for a "good first issue" and have a look at the developer documentation.

If you have a feature that you would like to see implemented, create an issue!


ProbDiffEq curates a range of benchmarks that includes various library-internal configurations but also other packages like SciPy, JAX, or Diffrax. To run the benchmark locally, install all dependencies via

pip install .[example,test]
and then either open Jupyter and go to docs/benchmarks or execute all benchmarks via
make run-benchmarks
Be patient, it might take a while. Afterwards, open Jupyter to look at the result or build the documentation via
mkdocs serve
What do you find?

Similar projects¤

Check out how to transition from those packages: link.

Anything missing in this list? Please open an issue or make a pull request.

You might also like¤

  • diffeqzoo: A library for example implementations of differential equations in NumPy and JAX
  • probfindiff: Probabilistic numerical finite differences, in JAX.