A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions
This work addresses computational bottlenecks for geochemical simulations in nuclear waste disposal safety assessments, though it is incremental as it applies a recently popular method to a new domain.
The paper tackles the high computational cost of geochemical solvers in reactive transport simulations by proposing a Kolmogorov-Arnold network surrogate model, which reduces errors by 62% and 59% compared to multilayer perceptrons on a cement benchmark and maintains median errors near 1e-3 for radium solid solution models.
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)SO$_4$ and ternary (Sr,Ba,Ra)SO$_4$ 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 $1\times10^{-3}$. 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.