Multi-Scale Cross-attention and Time-aware GAN Surrogate for Solute Transport Simulation in in-situ Uranium Leaching

Reactive transport models (RTMs) are widely used to simulate coupled flow-transport-reaction processes in in-situ uranium leaching (ISL). However, high-resolution discretization, strong medium heterogeneity, and long simulation horizons often render RTMs computationally expensive, which limits their applicability in computation-intensive tasks such as long-term forecasting, large-scale scenario screening, and uncertainty quantification. In recent years, image-regression-based surrogate models were explored to reduce computational cost. Nevertheless, when temporal representation is weak and explicit cross-time consistency constraints are absent, surrogates may exhibit noticeable accuracy fluctuations at time points not involved in supervision, especially for interpolation time within a long simulation horizon. To address these limitations, MCFT-GAN, a generative adversarial network (GAN) surrogate was proposed, which integrates multi-scale cross-attention with a time-aware conditioning mechanism for sequence-level prediction of reactive solute transport in ISL. This framework was engineered to achieve two core objectives: First, it boosts multi-scale spatial feature fusion through cross-attention, enabling the simultaneous capture of local details and global plume structures; Second, it enhances temporal generalization performance by explicitly embedding temporal information into the network architecture and imposing regularization constraints on predictive outputs across discrete time stamps. Specifically, MCFT-GAN incorporates time-aware conditioning to guide the generation process at specified time stages and introduces a cross-time consistency strategy to stabilize temporal evolution and mitigate performance degradation at unseen time points. A site-scale RTM for uranium reactive transport was established based on operating conditions from a sandstone-hosted uranium deposit in Inner Mongolia. Using this RTM, a 650 d numerical simulation campaign was conducted and a spatiotemporal dataset was constructed to capture the full-cycle dynamic evolution of concentration fields. The dataset was used for training and testing the surrogate, with particular attention to evaluate performance at interpolation time points that were excluded from direct supervision. Experimental results demonstrate that MCFT-GAN achieves high predictive accuracy on the test set and maintains accuracy levels at interpolation time points comparable to those at supervised training time points, indicating improved temporal generalization. At the sequence-distribution level, MCFT-GAN attains a Fréchet video distance (FVD) of 39.224, outperforming the baseline conditional deep convolutional GAN (cDC-GAN, FVD=56.847), which suggests a closer match between generated sequences and RTM reference sequences in the spatiotemporal feature space. In terms of computational efficiency, MCFT-GAN requires approximately 0.093 s to infer concentration fields at 14 time points for a single scenario, yielding an acceleration of about 1.1×10⁴ relative to the RTM runtime (about 17 min). These results indicate that MCFT-GAN provides a low-cost, sequence-level surrogate capable of supporting computation-intensive RTM applications for complex reactive solute transport problems.