Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation

2026-05-11

AI Summary

This work addresses the lack of a unified understanding and reliable quantification of uncertainty in machine learning models applied to physical sciences, which undermines the credibility of scientific discovery. The authors propose a comprehensive uncertainty classification framework tailored to the intersection of physics and artificial intelligence, systematically clarifying the distinctions between predictive and inferential uncertainty from both Bayesian and frequentist perspectives. The framework integrates multidimensional validation techniques—including coverage, probabilistic calibration, bias diagnostics, and proper scoring rules—to rigorously assess uncertainty quality. Its effectiveness is demonstrated through representative regression and classification case studies, offering a structured and actionable guideline for evaluating uncertainty in AI-driven physical science applications.

Abstract

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for physics, introducing a unified taxonomy of uncertainty and clarifying the interpretation of predictive and inference uncertainties across frequentist and Bayesian frameworks. We discuss principled validation tools, including coverage, calibration, bias tests, and proper scoring rules, and illustrate them with simple regression and classification examples.

Problem

• uncertainty quantification
• machine learning
• physics
• probabilistic statements
• validation

Innovation

• uncertainty quantification
• taxonomy
• Bayesian inference
• calibration
• proper scoring rules