mlsanityData to 7 Oct 2026

ProbNum: Probabilistic Numerics in Python

arXiv 2112.02100 ↗First posted 3 Dec 2021cs.MS cs.LG cs.NAcited by 10

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Abstract (arXiv)

Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential equation simulation. PNMs naturally incorporate prior information about a problem and quantify uncertainty due to finite computational resources as well as stochastic input. In this paper, we present ProbNum: a Python library providing state-of-the-art probabilistic numerical solvers. ProbNum enables custom composition of PNMs for specific problem classes via a modular design as well as wrappers for off-the-shelf use. Tutorials, documentation, developer guides and benchmarks are available online at www.probnum.org.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 13 of its 27 references that are in the map. First posted on arXiv 3 Dec 2021.

Builds on

13 of 27 references.

References · 13

  1. 2018Pyro: Deep Universal Probabilistic Programmingcited by 379
  2. 2019Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyrocited by 187
  3. 2015Probabilistic Numerics and Uncertainty in Computationscited by 59
  4. 2017Bayesian Probabilistic Numerical Methodscited by 50
  5. 2018Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspectivecited by 31
  6. 2021Emulation of physical processes with Emukitcited by 24
  7. 2020Calibrated Adaptive Probabilistic ODE Solverscited by 21
  8. 2021A Probabilistic State Space Model for Joint Inference from Differential Equations and Datacited by 21
  9. 2020Bayesian ODE Solvers: The Maximum A Posteriori Estimatecited by 19
  10. 2019A Modern Retrospective on Probabilistic Numericscited by 18
  11. 2014Probabilistic Interpretation of Linear Solverscited by 12
  12. 2020Probabilistic Linear Solvers for Machine Learningcited by 10
1 more
  1. 2018A Bayesian Conjugate Gradient Methodcited by 7

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Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 3; 2025: 3.

10 papers.

  1. 2022Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solverscited by 40
  2. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  3. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  4. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  5. 2024Conditional Bayesian Quadraturecited by 8
  6. 2025Nested Expectations with Kernel Quadraturecited by 5
  7. 2023Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equationscited by 3
  8. 2024Scaling up Probabilistic PDE Simulators with Structured Volumetric Informationcited by 2
  9. 2024Adaptive Probabilistic ODE Solvers Without Adaptive Memory Requirementscited by 0
  10. 2025Propagating Model Uncertainty through Filtering-based Probabilistic Numerical ODE Solverscited by 0