Coarse-scale Parameters Research Articles

Prediction of Discretization of GMsFEM Using Deep Learning

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media (various permeability fields). The objective of our work is to use deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.

Upscaled HDG Methods for Brinkman Equations with High-Contrast Heterogeneous Coefficient

In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that depend on the high-contrast coefficient weakly. Due to the heterogeneity of the problem, a huge global system will be produced after the numerical discretization of HDG method. Thanks to the upscaled structure of the proposed methods, we are able to reduce the huge global system onto the skeleton of the coarse mesh only while still capturing important fine scale features of this problem. The finite element space over the coarse mesh is irrelevant to the fine scale computation. This feature makes our proposed method very attractive. Several numerical examples are presented to support our theoretical findings.

Ensemble level upscaling for compositional flow simulation

Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. We apply a newly developed global compositional upscaling method to provide coarse-scale parameters and functions for selected realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of a-factors to capture component fluxes. Additional features include near-well upscaling for all coarse parameters and functions, and iteration on the a-factors, which is shown to improve accuracy. In the EnLU framework, this global upscaling is applied for only a few selected realizations. For 90 % or more of the realizations, upscaled functions are assigned statistically based on quickly computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50, and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures.

Soil-vegetation type, stem density and species richness influence biomass of restored woodland in south-western Australia

Woody plantings are increasing across the globe to satisfy ecosystem service markets for carbon and ecological restoration. Assessments of these complex woody systems typically use coarse-scale parameters, based on the climate and soil type of a region, and/or remotely assessed vegetation cover, to estimate carbon in their above- and belowground biomass. However it remains poorly known what factors influence their biomass at finer scales. Here, we investigated biomass variability after five years across a 250ha environmental planting on a former agricultural property in south-western Australia. We aimed to understand which factors may influence observed biomass variability. The dominant canopy tree, Eucalyptus occidentalis, was planted as seedlings, and other woody species were direct sown in vegetation associations, according to soil type and landscape position, to reflect historic native assemblages. Results from 42 survey plots stratified across these associations showed variable seedling establishment from the seed mix, and that the amount of above- and belowground biomass varied widely (Coefficient of variation=60%). A site mean and standard error were inadequate to capture biomass distribution. Instead, two modes were evident within the distribution at approximately 5Mgha−1 and 15Mgha−1 with variation primarily associated with differential seedling establishment and growth across the vegetation associations. Additionally, multiple regression analysis showed that stem density explained a significant amount of biomass variation whilst greater species richness was associated with increased biomass once stem density had been accounted for – models combining soil-vegetation association, number of individuals, and species richness explained between 60% and 80% of biomass variation depending on the response variable (total or live biomass) and choice of allometric equations to predict biomass. There was some evidence for a role of nitrogen-fixing species in determining biomass variation. There was no evidence for biomass variation being explained by the proportional contribution of the dominant canopy tree (E. occidentalis) or eucalypts in general once number of individuals had been accounted for, despite their large contribution to plot biomass. The substantial variation we show across the site has implications for carbon accounting practices and cost-benefit analyses guiding investment and regulation of the sector. Our results add weight to emerging evidence that restoring woody plant diversity can be compatible with efforts to maximize biomass and show the potential for diverse restored woodland assemblages to meet developing market demands for carbon.

Can remote sensing estimate fine-scale quality indicators of natural habitats?

Efficient management and conservation of natural habitats requires a thorough knowledge and sustained monitoring of their ecological quality. In recent years, several methods have been developed to assess the local conservation status in the field. These typically combine estimates of coarse-scale indicators, such as tree and grass encroachments, with very fine-scale indicators that require precise fieldwork, such as the number of key species present. We first tested whether coarse-scale field characteristics can provide information on fine-scale indicators. Then, this idea was extended to remote sensing techniques to derive estimates of fine-scale properties that cannot be derived directly by the sensors. The method was elaborated for two Natura 2000 heathland areas, combining field conservation status assessments of over 650 locations with remote sensing information derived from an airborne hyperspectral scanner image. Boosted regression trees using field estimates of coarse-scale parameters as predictors were able to explain up to 43% of the variation in the fine-scale indicators. When using remote sensing data, models performed only slightly less. Up to 35% of the variation was explained using remote sensing estimates of coarse-scale parameters as predictors, and up to 39% was explained when additional remotely sensed land cover data were included in the models. Although these rates are not high in absolute terms, model predictions for certain parameters were more precise than field estimates, especially for criteria with a high between-observer variability. These results clearly illustrate the potential of remote sensing imagery to derive information on the conservation status of habitats, even for fine-scale elements that are too small to be derived directly.