# A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions

arXiv: https://arxiv.org/abs/2603.15307 · HTML: https://mlsanity.com/paper/2603.15307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 63 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability](https://mlsanity.com/paper/2407.11075/) (2024)
- [SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.06286/) (2024)
- [Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classification](https://mlsanity.com/paper/2411.14904/) (2024)
- [Rapid modelling of reactive transport in porous media using machine learning: limitations and solutions](https://mlsanity.com/paper/2405.14548/) (2024)

## Abstract (arXiv)

The computational cost of geochemical solvers is a challenging matter. For reactive transport simulations, where chemical calculations are performed up to billions of times, it is crucial to reduce the total computational time. Existing publications have explored various machine-learning approaches to determine the most effective data-driven surrogate model. In particular, multilayer perceptrons are widely employed due to their ability to recognize nonlinear relationships. In this work, we focus on the recent Kolmogorov-Arnold networks, where learnable spline-based functions replace classical fixed activation functions. This architecture has achieved higher accuracy with fewer trainable parameters and has become increasingly popular for solving partial differential equations. First, we train a surrogate model based on an existing cement system benchmark. Then, we move to an application case for the geological disposal of nuclear waste, i.e., the determination of radionuclide-bearing solids solubilities. To the best of our knowledge, this work is the first to investigate co-precipitation with radionuclide incorporation using data-driven surrogate models, considering increasing levels of thermodynamic complexity from simple mechanical mixtures to non-ideal solid solutions of binary (Ba,Ra)SO4 and ternary (Sr,Ba,Ra)SO4 systems. On the cement benchmark, we demonstrate that the Kolmogorov-Arnold architecture outperforms multilayer perceptrons in both absolute and relative error metrics, reducing them by 62% and 59%, respectively. On the binary and ternary radium solid solution models, Kolmogorov-Arnold networks maintain median prediction errors near 1×10-3. This is the first step toward employing surrogate models to speed up reactive transport simulations and optimize the safety assessment of deep geological waste repositories.