Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

Evaluating uncertainty in ${\mathrm{CO}}_2$ injection projections often requires numerous high-resolution geological realizations (GRs) which, although effective, are computationally demanding. This study proposes the use of representative geological realizations (RGRs) as an efficient approach to capture the uncertainty range of the full set while reducing computational costs. A predetermined number of RGRs is selected using an integrated unsupervised machine learning (UML) framework, which includes Euclidean distance measurement, multidimensional scaling (MDS), and a deterministic K-means (DK-means) clustering algorithm. In the context of the intricate 3D aquifer ${\mathrm{CO}}_2$ storage model, PUNQ-S3, these algorithms are utilized. The UML methodology selects five RGRs from a pool of 25 possibilities (20% of the total), taking into account the reservoir quality index (RQI) as a static parameter of the reservoir. To determine the credibility of these RGRs, their simulation results are scrutinized through the application of the Kolmogorov–Smirnov (KS) test, which analyzes the distribution of the output. In this assessment, 40 ${\mathrm{CO}}_2$ injection wells cover the entire reservoir alongside the full set. The end-point simulation results indicate that the ${\mathrm{CO}}_2$ structural, residual, and solubility trapping within the RGRs and full set follow the same distribution. Simulating five RGRs alongside the full set of 25 GRs over 200 years, involving 10 years of ${\mathrm{CO}}_2$ injection, reveals consistently similar trapping distribution patterns, with an average value of $D_{\max }$ of 0.21 remaining lower than $D_{\mathrm{critical}}$ (0.66). Using this methodology, computational expenses related to scenario testing and development planning for ${\mathrm{CO}}_2$ storage reservoirs in the presence of geological uncertainties can be substantially reduced.

Climate change research uses an ensemble of general circulation model runs (GCMs-runs) to predict future climate under uncertainties. To reduce computational costs, this study selects representative GCM-runs (RGCM-runs) for Western North America (WNA) based on their performance in replicating historical climate conditions from 1981 to 2005 and projecting future changes from 1981–2010 to 2071–2100. This evaluation is conducted under two representative concentration pathways (RCPs) scenarios, RCP4.5 and RCP8.5, from the Coupled Model Intercomparison Project 5. By using an envelope-based selection technique and a multi-objective distance-based approach, we identify four RGCM-runs per RCP representing diverse climatic conditions, including wet-warm, wet-cold, dry-warm, and dry-cold. Compared to the full-set, these selected runs show a decreased mean absolute error (MAE) between the reference and RGCM-runs concerning the monthly average mean air temperature (T̄) and precipitation (P̄). For RCP4.5, T̄ MAE is 0.45 (vs. 0.58 in the full-set) and P̄ MAE is 0.31 (vs. 0.42). For RCP8.5, T̄ MAE is 0.51 (vs. 0.75) and P̄ MAE is 0.25 (vs. 0.36). The lower MAE values in the RGCM-run set indicate closer alignment between predicted and reference values, making the RGCM-run suitable for climate impact assessments in the region.