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Heterogeneity and a paucity of measurements of key material properties undermine the veracity of quantitative predictions of subsurface flow and transport. For such model forecasts to be useful as a management tool, they must be accompanied by computationally expensive uncertainty quantification, which yields confidence intervals, probability of exceedance, and so forth. We design and implement novel multilevel Monte Carlo (MLMC) algorithms that accelerate estimation of the cumulative distribution functions (CDFs) of quantities of interest, for example, water breakthrough time or oil production rate. Compared to standard non-smoothed MLMC, the new estimators achieve a significant variance reduction at each discretization level by smoothing the indicator function with a Gaussian kernel or replacing standard Monte Carlo (MC) with the recently developed hierarchical Latinized stratified sampling (HLSS). After validating the kernel-smoothed MLMC and HLSS-enhanced MLMC methods on a single-phase flow test bed, we demonstrate that they are orders of magnitude faster than standard MC for estimating the CDF of breakthrough times in multiphase flow problems.

Accurate renewable energy production forecasting has become a priority as the share of intermittent energy sources on the grid increases. Recent work has shown that convolutional deep learning models can successfully be applied to forecast weather maps. Building on this capability, a ResNet‐inspired model that estimates solar and wind power production based on weather maps is proposed. By capturing both spatial and temporal correlations using convolutional neural networks with stacked input frames, the model is designed to capture the complex dynamics governing these energy sources. A dataset that focuses on the state of California is constructed and made available as a secondary contribution of the work. It is demonstrated that the novel model outperforms traditional deep learning techniques: it predicts an accurate power production profile that is smooth and includes high‐frequency details.

A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.