InterPore2026

Operator Learning for Multispecies Reactive Transport in Heterogeneous Media

19 May 2026, 14:50

15m

Oral Presentation (MS15) Machine Learning in Porous Media MS15

Speaker

Mrs Fatima Tokmukhamedova (La rochelle University)

Description

Coastal protection structures face increasing challenges from sea level rise, extreme weather events, and material degradation [1]. Innovative approaches such as cathodic protection, which induces the precipitation of calco-magnesian deposits (e.g., brucite and aragonite), provide promising strategies for reinforcing marine infrastructures in a sustainable manner [2-3]. However, the long-term durability of these deposits depends strongly on their evolving porosity, mineral balance, and transport–reaction processes [4]. Accurate prediction of this evolution is therefore crucial for assessing future stability of coastal protection measures.
Simulating these processes requires solving coupled nonlinear partial differential equations describing multispecies diffusion-reaction kinetics in heterogeneous media. Traditional direct numerical approaches, such as finite-difference, finite-volume, finite-element, or spectral methods, deliver accurate results but are computationally expensive, particularly when applied to long-time evolution, parameter studies (with significant number of species) [5].
To address these limitations, recent advances in operator-learning neural networks offer surrogate modeling approaches that learn mappings between function spaces and enable generalization across heterogeneous porous media [6–9]. In this work, operator learning is investigated as a surrogate modeling strategy for multispecies reactive transport in heterogeneous media. The governing dynamics are described by coupled diffusion–reaction equations with spatially varying transport properties derived from heterogeneous porosity fields. Numerical simulations are used to generate reference datasets capturing nonlinear spatiotemporal concentration dynamics under reaction-dominated regimes. A class of neural operator models is evaluated, with integral-transform-based formulations operating in latent spaces, where the learned integral operators may be linear or nonlinear [9]. These models are trained to advance the system in time and subsequently rolled out for temporal prediction.
Using this framework, model performance is assessed through quantitative error metrics and qualitative comparisons of spatial concentration patterns over extended time horizons. The results indicate that integral-transform-based operator models can achieve performance comparable to Fourier-based neural operators for multispecies reactive transport problems. In particular, learned integral kernels provide additional flexibility for representing high-frequency spatial features, which are not efficiently represented by Fourier-based neural operator models. Similar performance is observed with a reduced number of model parameters, motivating continued efforts toward improving accuracy and stability through architectural and training refinements.
Taken together, these results indicate that integral-transform-based operator learning may complement existing neural operator models in reactive transport applications.