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ProbNum: Probabilistic Numerics in Python [article]

Jonathan Wenger, Nicholas Krämer, Marvin Pförtner, Jonathan Schmidt, Nathanael Bosch, Nina Effenberger, Johannes Zenn, Alexandra Gessner, Toni Karvonen, François-Xavier Briol, Maren Mahsereci, Philipp Hennig
2021 arXiv   pre-print
In this paper, we present ProbNum: a Python library providing state-of-the-art probabilistic numerical solvers.  ...  Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.  ...  4 ProbNum: Probabilistic Numerics in Python the functionality of probabilistic numerical methods.  ... 
arXiv:2112.02100v1 fatcat:beroko2yb5dmbcwdwumhsju5sy

Stable Implementation of Probabilistic ODE Solvers [article]

Nicholas Krämer, Philipp Hennig
2020 arXiv   pre-print
However, these algorithms suffer from numerical instability when run at high order or with small step-sizes -- that is, exactly in the regime in which they achieve the highest accuracy.  ...  Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems.  ...  the Nordsieck-transformation that is mentioned by , a variant of which has been used in ProbNum, a collection of probabilistic numerical algorithms in Python.  ... 
arXiv:2012.10106v1 fatcat:nsrhmvxtynfyddufzmmrd4h3qa

Black Box Probabilistic Numerics [article]

Onur Teymur, Christopher N. Foley, Philip G. Breen, Toni Karvonen, Chris. J. Oates
2021 arXiv   pre-print
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved.  ...  A convergent sequence of approximations to the quantity of interest constitute a dataset, from which the limiting quantity of interest can be extrapolated, in a probabilistic analogue of Richardson's deferred  ...  The authors wish to thank Jon Cockayne and Ilse Ipsen for feedback on earlier versions of the manuscript, and Nicholas Krämer for assistance with the probnum package.  ... 
arXiv:2106.13718v2 fatcat:3ru66amt6basllwduskkkn6kay

Probabilistic Numerical Methods - From Theory to Implementation (Dagstuhl Seminar 21432)

Philipp Hennig, Ilse C.F. Ipsen, Maren Mahsereci, Tim Sullivan
2022
Probabilistic numerical methods aim to explicitly represent uncertainty resulting from limited computational resources and imprecise inputs in these models.  ...  foundation for a software stack for probabilistic numerical methods.  ...  ProbNum: Probabilistic numerics in Python. arxiv preprint, 2021.  ... 
doi:10.4230/dagrep.11.9.102 fatcat:gcy24u6x75cajcb34es47ywsx4

Testing whether a Learning Procedure is Calibrated [article]

Jon Cockayne, Matthew M. Graham, Chris J. Oates, T. J. Sullivan, Onur Teymur
2022 arXiv   pre-print
A hypothesis-testing framework is developed in order to assess, using simulation, whether a learning procedure is calibrated.  ...  This paper studies conditions for a learning procedure to be considered calibrated, in the sense that the true data-generating parameters are plausible as samples from its distributional output.  ...  TJS has been supported in part by the German Research Foundation (Deutsche Forschungsgemeinschaft) through project 415980428 and the Excellence Cluster "MATH+ The Berlin Mathematics Research Centre" (EXC  ... 
arXiv:2012.12670v5 fatcat:r6s7yqirijcpneiphidy7xpb4q

GaussED: A Probabilistic Programming Language for Sequential Experimental Design [article]

Matthew A. Fisher, Onur Teymur, Chris. J. Oates
2021 arXiv   pre-print
Motivated by the diverse problems that can in principle be solved with common code, this paper presents GaussED, a simple probabilistic programming language coupled to a powerful experimental design engine  ...  , which together automate sequential experimental design for approximating a (possibly nonlinear) quantity of interest in Gaussian processes models.  ...  Acknowledgements MAF was supported by the EPSRC Centre for Doctoral Training in Cloud Computing for Big Data EP/L015358/1 at Newcastle University, UK.  ... 
arXiv:2110.08072v1 fatcat:qbkzxkjyfbbe7kloxw5wlsj7ca

Dagstuhl Reports, Volume 11, Issue 9, September 2019, Complete Issue [article]

2022
So how can we design something in the middle?  ...  The research question now is, how can we modify/extend the tools we currently have in order to check the stated problem?  ...  Bayesian BayesCG: A probablistic numeric linear solver ProbNum is a Python library that provides probabilistic numerical solvers to a wider audience.  ... 
doi:10.4230/dagrep.11.9 fatcat:ahz57d6jknd7rf66xbkwcwxmxq