# Baseflow identification via explainable AI with Kolmogorov-Arnold networks

arXiv: https://arxiv.org/abs/2410.11587 · HTML: https://mlsanity.com/paper/2410.11587/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 10 Oct 2024.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression](https://mlsanity.com/paper/2302.00773/) (2023)
- [Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems](https://mlsanity.com/paper/2206.00669/) (2022)

## Built on by (most cited first, 1 of 1)

- [Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics](https://mlsanity.com/paper/2412.04845/) (2024)

## Abstract (arXiv)

Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov-Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN-derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts. On a test set, they increase the Nash-Sutcliffe Efficiency (NSE) by 67%, decrease the root mean squared error by 30%, and increase the Kling-Gupta efficiency by 24%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water-balance equation at the mean-annual scale. The KAN-derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN-derived equations based on the original water balance. While the performance of our model and tree-based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes.