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probabilistic numerics

Learn to Approximate. Approximate to Learn.

Probabilistic Numerics in Python.

ProbNum is a Python toolkit for solving numerical problems in linear algebra, optimization, quadrature and differential equations. ProbNum solvers not only estimate the solution of the numerical problem, but also its uncertainty (numerical error) which arises from finite computational resources, discretization and stochastic input. This numerical uncertainty can be used in downstream decisions.

Currently, available solvers are:

  • Linear solvers: Solve $A x = b$ for $x$.
  • ODE solvers: Solve $\dot{y}(t) = f(y(t), t)$ for $y$.
  • Integral solvers (quadrature): Solve $F = \int_D f(x) \mathrm{d}p(x)$ for $F$.

Lower level structure includes:

  • Random variables and random processes, as well as arithmetic operations thereof.
  • Memory-efficient and lazy implementation of linear operators.
  • Filtering and smoothing for (probabilistic) state-space models, mostly variants of Kalman filters.

ProbNum is underpinned by the research field probabilistic numerics (PN), which lies at the intersection of machine learning and numerics. PN aims to quantify uncertainty arising from intractable or incomplete numerical computation and from stochastic input using the tools of probability theory. The general vision of probabilistic numerics is to provide well-calibrated probability measures over the output of a numerical routine, which then can be propagated along the chain of computation.


To get started install ProbNum using pip.

pip install probnum

Alternatively, you can install the latest version from source.

pip install git+

Note: This package is currently work in progress, therefore interfaces are subject to change.

Documentation and Examples

For tips on getting started and how to use this package please refer to the documentation. It contains a quickstart guide and Jupyter notebooks illustrating the basic usage of the ProbNum solvers.

Package Development

This repository is currently under development and benefits from contribution to the code, examples or documentation. Please refer to the contribution guidelines before making a pull request.

A list of core contributors to ProbNum can be found here.

Citing ProbNum

If you are using ProbNum in your research, please cite as provided. The "Cite this repository" button on the sidebar generates a BibTeX entry or an APA entry.

License and Contact

This work is released under the MIT License.

Please submit an issue on GitHub to report bugs or request changes.