mlsanityData to 14 Oct 2026

A Modern Retrospective on Probabilistic Numerics

arXiv 1901.04457 ↗First posted 14 Jan 2019math.NA cs.NA math.HOcited by 18

Not on the map. Why?

Abstract (arXiv)

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). First posted on arXiv 14 Jan 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 4; 2024: 3; 2025: 1; 2026: 3.

18 papers.

Sort:

  1. 2024Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AIcited by 62
  2. 2022Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solverscited by 41
  3. 2022Posterior and Computational Uncertainty in Gaussian Processescited by 24
  4. 2021Bayesian Numerical Methods for Nonlinear Partial Differential Equationscited by 15
  5. 2022Fenrir: Physics-Enhanced Regression for Initial Value Problemscited by 11
  6. 2021ProbNum: Probabilistic Numerics in Pythoncited by 10
  7. 2024Conditional Bayesian Quadraturecited by 9
  8. 2021Pick-and-Mix Information Operators for Probabilistic ODE Solverscited by 6
  9. 2023Probabilistic Exponential Integratorscited by 4
  10. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  11. 2023Parallel-in-Time Probabilistic Numerical ODE Solverscited by 3
  12. 2024Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanicscited by 3
6 more
  1. 2023Accelerating Non-Conjugate Gaussian Processes By Trading Off Computation For Uncertaintycited by 2
  2. 2026Bayesian Quadraturecited by 1
  3. 2021Black Box Probabilistic Numericscited by 0
  4. 2025Learning Geometric-Aware Quadrature Rules for Functional Minimizationcited by 0
  5. 2026Machine learning assisted state prediction of misspecified linear dynamical system via modal reductioncited by 0
  6. 2026Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEscited by 0