# Distribution-Free Conformal Prediction for Steel Fatigue Strength: Marginal Validity Is Not Enough

arXiv: https://arxiv.org/abs/2608.07589 · HTML: https://mlsanity.com/paper/2608.07589/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Materials Property Prediction with Uncertainty Quantification: A Benchmark Study](https://mlsanity.com/paper/2211.02235/) (2022)
- [Uncertainty Prediction for Machine Learning Models of Material Properties](https://mlsanity.com/paper/2107.07997/) (2021)

## Abstract (arXiv)

Predicting fatigue failure in steel components experimentally is costly, requiring testing across multiple compositions and processing conditions, spurring research on data-driven prediction models. Studies using the NIMS MatNavi steel fatigue dataset often report high point-prediction accuracy but rely on aggregate error metrics, leaving uncertainty about the reliability of individual predictions and whether accuracy is consistent across the fatigue-strength spectrum. This paper is the first to apply conformal prediction to steel fatigue strength, comparing seven interval-construction methods across 50 independent data splits and distinguishing marginal coverage from coverage within specific sub-regions of the predicted property. A gradient-boosting point model achieves an R^2 of 0.976 +/- 0.009 and a mean absolute error of 18.3 +/- 2.3 MPa. Split-conformal prediction provides valid marginal coverage (0.918) but drops to 0.758 in the highest-strength quartile, where design margins are most critical, a pattern also observed with a Gaussian process baseline. Two locally-adaptive methods correct this: a cross-fitted normalised conformal method holds 0.872-0.940 across quartiles at no cost in average width, and Mondrian group-conditional conformal prediction holds the tightest band of any method (0.917-0.939) at a 12% width premium, part of which traces to the more conservative finite-sample quantile level implied by per-group calibration at this sample size. Conformalized quantile regression, by contrast, restores marginal validity but inflates intervals in every quartile without closing the conditional gap. Marginal coverage claims for ML-based fatigue-strength predictions can conceal systematic unreliability precisely where engineering decisions are most risky; therefore, conditional coverage should be routinely assessed alongside marginal coverage.