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Explainable AI for transportation process management: symbolic regression of freight train speeds using Kolmogorov–Arnold networks (KANs)

Sergey E. Eliseev Nikolay A. Davydov Mikhail P. Noskov Sergey V. Eroshenko
Aug 2026 · Railway Sciences · 0 citations · 13 references

TL;DR

Beyond the first railway application of KAN, the study presents a complete framework for explainable capacity management: it shows how a single KAN model can be distilled into a human-readable, operationally meaningful equation that quantifies nonlinear, asymptotic and interaction effects – a capability not offered by post hoc explainable artificial intelligence methods.

Abstract

This study addresses the black-box problem in railway predictive analytics by applying Kolmogorov–Arnold networks (KANs) to freight train speed prediction. The aim is to obtain not only an accurate forecast, but also an analytical expression that can support transparent operational and managerial decisions. A comparative analysis of five approaches is conducted: linear regression, gradient boosting (CatBoost), multi-layer perceptron (MLP), symbolic regression using genetic programming (gplearn) and the proposed KAN architecture. The dataset comprises 55,508 observations with 23 operational and infrastructure factors. Three cross-validation strategies (random, time-based and track-stratified) and the Friedman test are employed. Symbolic formulas are extracted from linear regression, KAN and gplearn. The trained KAN model (before symbolic extraction) achieves RMSE = 4.12–4.25, comparable to CatBoost (3.87–3.98) and superior to MLP (4.53–4.68). An analytical formula containing exponential, logarithmic and polynomial terms is successfully extracted from KAN. The RMSE of the KAN-derived formula is 13% lower than that of linear regression and 14% lower than that of gplearn on the full 23-feature set. The results confirm that KAN can capture complex dependencies while remaining analytically interpretable. The study presents a complete framework for explainable capacity management, offering a human-readable equation that quantifies nonlinear, asymptotic and interaction effects. Beyond the first railway application of KAN, the study presents a complete framework for explainable capacity management: it shows how a single KAN model can be distilled into a human-readable, operationally meaningful equation that quantifies nonlinear, asymptotic and interaction effects – a capability not offered by post hoc explainable artificial intelligence methods. The resulting expressions can directly inform timetable optimisation, infrastructure investment appraisal and operational scenario analysis.

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