v271: Proceedings of ProbNum 2025

2026-06-04 · Source: Proceedings of Machine Learning Research · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

Volume 271 presents the proceedings of the First International Conference on Probabilistic Numerics, held from 1-3 September 2025, at EURECOM in Sophia Antipolis, France. Edited by Motonobu Kanagawa, Jon Cockayne, Alexandra Gessner, and Philipp Hennig, this collection features diverse research advancing the field. Key contributions include methods for fixing pitfalls in probabilistic time-series forecasting evaluation using kernel quadrature, and novel adaptive probabilistic ODE solvers designed to operate without adaptive memory requirements. Other papers explore propagating model uncertainty through filtering-based ODE solvers, fast Gaussian process regression for high-dimensional functions with derivative information, and the integration of Natural Evolutionary Search with probabilistic numerics. Further research covers randomised postiterations for Calibrated BayesCG, a dictionary of closed-form kernel mean embeddings, and applications like solving Einstein’s equations as Bayesian inference. The volume also addresses practical aspects such as online conformal probabilistic numerics via adaptive edge-cloud offloading.

Key takeaway

For research scientists and AI practitioners exploring robust numerical methods, this collection highlights critical advancements in Probabilistic Numerics. You should consider integrating uncertainty quantification techniques, such as adaptive probabilistic ODE solvers or kernel mean embeddings, into your models to enhance reliability and interpretability. The diverse applications, from time-series forecasting to solving Einstein's equations, suggest broad utility. Explore specific papers to identify methods applicable to your domain, particularly for high-dimensional functions or systems requiring rigorous uncertainty propagation.

Key insights

Probabilistic Numerics integrates uncertainty quantification into numerical algorithms for robust computation.

Principles

• Quantify uncertainty in numerical computations.
• Improve robustness of numerical methods.
• Integrate Bayesian inference into algorithms.

In practice

• Evaluate time-series forecasts with kernel quadrature.
• Solve ODEs with adaptive memory-efficient methods.
• Apply Bayesian inference to physical equations.

Topics

• Probabilistic Numerics
• ODE Solvers
• Gaussian Process Regression
• Bayesian Inference
• Uncertainty Quantification
• Kernel Methods

Code references

• pnkraemer/code-adaptive-prob-ode-solvers
• mmahsereci/kernel_embedding_dictionary

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Proceedings of Machine Learning Research.