scholarly journals Topological Analysis in Monte Carlo Simulation for Uncertainty Estimation

2019 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Jessell ◽  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Vitaliy Ogarko
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Topological Analysis ◽  
Uncertainty Estimation ◽  
Population Heterogeneity ◽  
Underlying Assumption ◽  
3D Geological Modeling ◽  
Plausible Model ◽  
Uncertainty Estimates

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for Uncertainty Estimation (MCUE) method. MCUE is a type of Bayesian Monte Carlo aimed at input data uncertainty propagation in implicit 3D geological modeling. In the Monte Carlo process, a series of statistically plausible models are built from the input data set which uncertainty is to be propagated to a final probabilistic geological model (PGM) or uncertainty index model (UIM). Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUE. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets’ variability and plausible model’s variability. Non-linearity is shown to arise from the effect of the geometrical ruleset on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces geological incompatibility and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUE is introduced. Boolean topological signatures recording lithological units’ adjacency are used as n-dimensional points to be considered individually or clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the PGMs and UIMs.

scholarly journals Topological analysis in Monte Carlo simulation for uncertainty propagation

Solid Earth ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 1663-1684 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Jessell ◽  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Vitaliy Ogarko
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Topological Analysis ◽  
Uncertainty Propagation ◽  
Population Heterogeneity ◽  
Plausible Model ◽  
Uncertainty Index ◽  
Uncertainty Estimates ◽  
Geological Models

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

scholarly journals Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Solid Earth ◽  
2018 ◽  
Vol 9 (2) ◽  
pp. 385-402 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Lindsay ◽  
Vitaliy Ogarko ◽  
Jeremie Giraud ◽  
Mark Jessell
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Structural Data ◽  
Uncertainty Estimation ◽  
Data Sets ◽  
Geological Modeling ◽  
Input Uncertainty ◽  
Wide Range ◽  
Geological Models

Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

scholarly journals Monte Carlo Simulations for Uncertainty Estimation in 3D Geological Modeling, A Guide for Disturbance Distribution Selection and Parameterization

2017 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Lindsay ◽  
Vitaliy Ogarko ◽  
Jeremie Giraud ◽  
Mark Jessell
Keyword(s):  
Monte Carlo ◽  
Input Data ◽  
Uncertainty Estimation ◽  
Data Sets ◽  
Geological Modeling ◽  
Data Set ◽  
Input Uncertainty ◽  
3D Geological Modeling ◽  
Wide Range ◽  
Geological Models

Abstract. Three-dimensional (3D) geological modeling aims to determine geological information in a 3D space using structural data (foliations and interfaces) and topological rules as inputs. They are necessary in any project where the properties of the subsurface matters, they express our understanding of geometries in depth. For that reason, 3D geological models have a wide range of practical applications including but not restrained to civil engineering, oil and gas industry, mining industry and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator’s parameterization) combined with input uncertainty (observational-, conceptual- and technical errors). Because 3D geological models are often used for impactful decision making it is critical that all 3D geological models provide accurate estimates of uncertainty. This paper’s focus is set on the effect of structural input data uncertainty propagation in implicit 3D geological modeling using GeoModeller API. This aim is achieved using Monte Carlo simulation uncertainty estimation (MCUE), a heuristic stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of inappropriate disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e. scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminishes the occurrence of artefacts.

scholarly journals Deep-learning-based membranous nephropathy classification and Monte-Carlo dropout uncertainty estimation

2021 ◽  
Author(s):  
Paulo Chagas ◽  
Luiz Souza ◽  
Izabelle Pontes ◽  
Rodrigo Calumby ◽  
Michele Angelo ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Nephrotic Syndrome ◽  
Deep Learning ◽  
Membranous Nephropathy ◽  
Uncertainty Estimation ◽  
Glomerular Diseases ◽  
Uncertainty Estimates ◽  
Model Predictions

Membranous Nephropathy (MN) is one of the most common glomerular diseases that cause adult nephrotic syndrome. To assist pathologists on MN classification, we evaluated three deep-learning-based architectures, namely, ResNet-18, DenseNet and Wide-ResNet. In addition, to accomplish more reliable results, we applied Monte-Carlo Dropout for uncertainty estimation. We achieved average F1-Scores above 92% for all models, with Wide-ResNet obtaining the highest average F1-Score (93.2%). For uncertainty estimation on Wide-ResNet, the uncertainty scores showed high relation with incorrect classifications, proving that these uncertainty estimates can support pathologists on the analysis of model predictions.

scholarly journals Application of Monte Carlo Simulation to Find Travel Time of Groundwater in the Iraqi Western Desert

2017 ◽  
Vol 8 (1) ◽  
pp. 17
Author(s):  
Dawood Eisa Sachit ◽  
Hayat Kareem Shukur Azawi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Distribution Function ◽  
Hydraulic Conductivity ◽  
Groundwater Flow ◽  
Travel Time ◽  
Input Data ◽  
Western Desert ◽  
Triangular Distribution ◽  
Entire Area

In this study, a computerized mathematical method represented by Monte Carlo simulation was used to predict the travel time of the groundwater flow in the Iraqi western desert. During the run of the simulations, all the hydraulic parameters of Darcy’s Law were fixed but the hydraulic conductivity. The input data of the hydraulic conductivity is compared to the triangular distribution function to find the best number of iteration to run the simulations. The results showed that an iteration number of 5000 was enough to achieve best match between the input data of the hydraulic conductivity and the fitted distribution function. In addition, the estimated travel time of the groundwater flow is broadly varied through the entire area and ranges from 1983 years to 113 741 years based on 10 000 m of travel distance. Furthermore, hydraulic conductivity of the aquifer has high impact on the estimated travel time of the groundwater flow. However, head difference of groundwater elevation among the selected wells considerably influences the expected travel time of the groundwater flow.

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