Ensemble Of Realizations Research Articles

Optimization of underground mining production layouts considering geological uncertainty using deep reinforcement learning

Mineral extraction plays a key role in the global raw materials supply chain, however the exhaustion of shallow deposits and typical scarcity of sampled data during exploration activities creates challenges in mine planning and design, where decision-making is highly sensitive to uncertainty in geology and mineral grade prediction. Geostatistical techniques are commonly used to generate a set of equiprobable simulated numerical models to capture these uncertainties, however incorporating these simulated models within a mine planning and design framework remains a major challenge. The purpose of this paper is to propose a novel approach to decision-making in underground mine design that can use information from an ensemble of numerical realizations of a mineral resource to improve the financial performance of the asset. A deep reinforcement learning (DRL) framework, using the proximal policy optimization (PPO) algorithm, is developed for the design of underground mining production level layouts. A case study is presented using a gold mineral resource characterized by an ensemble of 100 numerical realizations to verify the advantages of the proposed method, considering a baseline consisting of an industry standard automated design method. The DRL approach achieved an 8.3% higher expected profit, a 3.4% more gold mined than the baseline, and has the added functionality of considering uncertainty in mineral grades.

A theoretical model of excess attenuation of acoustic signals propagating under cracked sea-ice landscapes.

The Arctic sheet is transitioning from a continuous cover of thick multi-year ice to a fragmented landscape of thin young ice. If the type of acoustic transmission allows repetitive interaction of rays with the sea surface, in the fragmented scenario acoustic rays will undergo a random sequence of reflections from water or sea-ice interfaces. Calm sea conditions in the water channels between the ice floes (leads) and the smooth, flat surface of the young ice bottom reduce scattering due to interface roughness, resulting only in scattering due to inhomogeneity in surface reflectivity. Using an idealized framework, this study investigates the extent to which the mid- to high-frequency underwater acoustic propagation is altered due to repetitive interactions of acoustic signals with a sea surface consisting of a random distribution of ice sheets and leads. An expression for the coherent field (the acoustic field averaged over an ensemble of realizations of sea-ice distributions) was derived from theory. Any deviation from a homogeneous surface condition (either by randomly adding ice slabs in a free ice surface or by including leads in a fully ice-covered sea surface) leads to an excess attenuation of the coherent field. Results are validated by numerical simulations.

Isles of regularity in a sea of chaos amid the gravitational three-body problem

Context. The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. Aims. This study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Methods. Using three-body simulations performed with the accurate, regularized code TSUNAMI, we established criteria for identifying regular trajectories and analysed their impact on statistical outcomes. Results. Our analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Conclusions. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity.

Free Energy Differences in Nonequilibrium Thermodynamic Processes.

Systems which may be allowed to go out of equilibrium have been of interest recently. A quantity is formulated whose average over an ensemble of microscopic realizations of the process depends only on the initial and final states. This is so even though the system may not be in equilibrium during the process. A generalization to the case where the initial and final states are not equilibrium states is developed here. Quantum analogues of these relations are derived, and an indication of how this might be applied to study entropy increase in thermodynamics is presented.

Characterizing the multisectoral impacts of future global hydrologic variability

There is significant uncertainty in how global water supply will evolve in the future, due to uncertain climate, socioeconomic, and land use change drivers and variability of hydrologic processes. It is critical to characterize the potential impacts of uncertainty in future water supply given its importance for food and energy production. In this work, we introduce a framework that integrates stochastic hydrology and human-environmental systems to characterize uncertainty in future water supply and its multisector impacts. We develop a global stochastic watershed model and demonstrate that this model can generate a large ensemble of realizations of basin-scale runoff with global coverage that preserves the mean, variance, and spatial correlation of a historical benchmark. We couple this model with a well-known human-environmental systems model to explore the impacts of runoff variability on the water and agricultural sectors across spatial scales. We find that the impacts of future hydrologic variability vary across sectors and regions. Impacts are felt most strongly in the water and agricultural sectors for basins that are expected to have unsustainable water use in the future, such as the Indus River basin. For this basin, we find that the variability in future irrigation water withdrawals and irrigated cropland increase over time due to uncertainty in renewable water supply. We also use the Indus basin to show how our stochastic ensemble can be leveraged to explore the global multisector consequences of local extreme runoff conditions. This work introduces a novel technique to explore the propagation of future hydrologic variability across human and natural systems and spatial scales.

Ensemble variational Bayesian approximation for the inversion and uncertainty quantification of Darcy flows in heterogeneous porous media with random parameters

The inversion and uncertainty quantification of physical parameters are important for many science and engineering problems. For nonlinear parameter inversion problems of flows in hydrocarbon reservoirs, estimating the true posterior probability distribution function for the random parameter is difficult when the dimension of the parameter is relatively high. Inversion methods such as gradient-based or heuristic optimization methods searching for the maximum a posterior are generally point-estimate, while uncertainty quantification using MCMC is computationally expensive. In the current study, a new ensemble variational Bayesian approximation method is developed to estimate the posterior probability density using an ensemble of realizations regarded as a trial sample distribution. The objective is to optimize the trial sample distribution such that the evidence lower bound is maximized indicating that the distance between the trial and true posterior distribution is minimized. A subspace is built using principle component analysis based on finite samples to obtain a diagonal positive-definite covariance matrix, and ensemble-based data assimilation is used to optimize the trial distribution efficiently. Heterogeneous 2D and 3D test cases of transient single- and two-phase Darcy flows are presented for validation.

Evaluation of data uncertainty for deep-learning-based CT noise reduction using ensemble patient data and a virtual imaging trial framework.

Deep learning-based image reconstruction and noise reduction (DLIR) methods have been increasingly deployed in clinical CT. Accurate assessment of their data uncertainty properties is essential to understand the stability of DLIR in response to noise. In this work, we aim to evaluate the data uncertainty of a DLIR method using real patient data and a virtual imaging trial framework and compare it with filtered-backprojection (FBP) and iterative reconstruction (IR). The ensemble of noise realizations was generated by using a realistic projection domain noise insertion technique. The impact of varying dose levels and denoising strengths were investigated for a ResNet-based deep convolutional neural network (DCNN) model trained using patient images. On the uncertainty maps, DCNN shows more detailed structures than IR although its bias map has less structural dependency, which implies that DCNN is more sensitive to small changes in the input. Both visual examples and histogram analysis demonstrated that hotspots of uncertainty in DCNN may be associated with a higher chance of distortion from the truth than IR, but it may also correspond to a better detection performance for some of the small structures.

Topological detection of phenomenological bifurcations with unreliable kernel density estimates

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations requires reliable kernel density estimates computed from an ensemble of system realizations. However, in several real world signals such as Big Data, only a single system realization is available—making it impossible to estimate a reliable kernel density. This study presents an approach for detecting P-type bifurcations using unreliable density estimates. The approach creates an ensemble of objects from Topological Data Analysis (TDA) called persistence diagrams from the system’s sole realization and statistically analyzes the resulting set. We compare several methods for replicating the original persistence diagram including Gibbs point process modelling, Pairwise Interaction Point Modelling, and subsampling. We show that for the purpose of predicting a bifurcation, the simple method of subsampling exceeds the other two methods of point process modelling in performance.

The Atacama Cosmology Telescope: map-based noise simulations for DR6

The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ∼ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code, mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

Epistemic modeling uncertainty of rapid neural network ensembles for adaptive learning

Emulator embedded neural networks, which are closely related to physics informed neural networks, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network model are trained with different random initializations. The ensemble of model realizations is used to assess epistemic modeling uncertainty caused by a lack of training samples. This uncertainty estimation is crucial information for successful goal-oriented adaptive learning in an aerospace system design exploration. However, the costs of training the ensemble models often become prohibitive and pose a computational challenge, especially when the models are not trained in parallel during adaptive learning. In this work, a new type of emulator embedded neural network is presented using the rapid neural network paradigm. Unlike the conventional neural network training that optimizes the weights and biases of all the network layers by using gradient-based backpropagation, rapid neural network training adjusts only the last layer connection weights by applying a linear regression technique. It is found that the proposed emulator embedded neural network trains near-instantaneously, typically without loss of prediction accuracy. The proposed method is demonstrated on multiple analytical examples, as well as an aerospace flight parameter study of a generic hypersonic vehicle.

Ice-flow model emulator based on physics-informed deep learning

Abstract Convolutional neural networks (CNN) trained from high-order ice-flow model realisations have proven to be outstanding emulators in terms of fidelity and computational performance. However, the dependence on an ensemble of realisations of an instructor model renders this strategy difficult to generalise to a variety of ice-flow regimes found in the nature. To overcome this issue, we adopt the approach of physics-informed deep learning, which fuses traditional numerical solutions by finite differences/elements and deep-learning approaches. Here, we train a CNN to minimise the energy associated with high-order ice-flow equations within the time iterations of a glacier evolution model. As a result, our emulator is a promising alternative to traditional solvers thanks to its high computational efficiency (especially on GPU), its high fidelity to the original model, its simplified training (without requiring any data), its capability to handle a variety of ice-flow regimes and memorise previous solutions, and its relatively simple implementation. Embedded into the ‘Instructed Glacier Model’ (IGM) framework, the potential of the emulator is illustrated with three applications including a large-scale high-resolution (2400x4000) forward glacier evolution model, an inverse modelling case for data assimilation, and an ice shelf.

A New Method for Postprocessing Numerical Weather Predictions Using Quantile Mapping in the Frequency Domain

Abstract Improving lead time for forecasting floods is important to minimize property damage and ensure the safety of the public and emergency services during flood events. Numerical weather prediction (NWP) models are important components of flood forecasting systems and have been vital in extending forecasting lead time under complex weather and terrain conditions. However, NWP forecasts still have significant uncertainty associated with the precipitation fields that are the main inputs of the hydrologic models and thus the resulting flood forecasts. An issue often overlooked is the importance of correctly representing variability over a range of different temporal scales. To address this gap, here a new wavelet-based method for postprocessing NWP precipitation forecasts is proposed. First, precipitation forecasts are decomposed into the frequency domain using a wavelet transform, providing estimates of the amplitudes and phases of the time series at different frequencies. Quantile mapping is then used to correct bias in the amplitudes of each frequency. Randomized phases are used to generate an ensemble of realizations of the precipitation forecasts. The postprocessed precipitation forecasts are reconstructed by taking the inverse of adjusted time-frequency decompositions with the corrected amplitudes and randomized phases. The proposed method was used to postprocess NWP precipitation forecasts in the Sydney region of Australia. There is a significant improvement in postprocessed precipitation forecasts across multiple time scales in terms of bias and temporal and spatial correlation structures. The postprocessed precipitation fields can be used for the modeling of fully distributed hydrologic systems, improving runoff stimulation, flood depth estimation, and flood early warning. Significance Statement A new method accounting for the timing and spatial errors of NWP precipitation forecasts is proposed, and it can improve the skill of forecasts across multiple time scales, especially at short lead times. The proposed method provides a practical and effective way to correct these errors by incorporating spatiotemporal neighborhood information through the frequency domain using sophisticated wavelet transforms. With systematic timing and spatial errors removed, precipitation forecasts will be more skillful, and hydrological modeling using the postprocessed forecasts can provide higher accuracy of streamflow estimation.

A new E‐OBS gridded dataset for daily mean wind speed over Europe

AbstractIn this paper we present daily mean wind speed as a new variable in the publicly accessible E‐OBS gridded datasets. Each of the variables in the E‐OBS dataset is provided at a spatial resolution of 0.1° × 0.1° and 0.25° × 0.25°. The variable “daily mean wind speed” starts from 1980 and is updated every month. The main method that we apply is the use of adaptive covariate selection to model the monthly mean wind speed as a function of covariates, like altitude, distance to coast and surface roughness. Then, we use Gaussian process regression to interpolate the daily anomalies from the station locations to the grid locations. In addition, we develop ensemble dispersion improvement auto‐tune (EDIT) to improve the reliability of the local ensemble spread. In order to communicate the methodological uncertainty in the resulting dataset, the E‐OBS wind speed grid is provided as a 20‐member ensemble of random realizations. As part of a preliminary analysis, we investigate the hypothesized wind speed stilling effect in recent decades. Indeed, we do find a small yet significant wind speed stilling effect in the E‐OBS dataset.

Synthesis of partially coherent Bessel-mode vortex-beams with radial coherence

Partially coherent Bessel-mode vortex-beams with radial coherence are introduced. The generated beams are fully coherent at pair of points along the same radial coordinate. The field is completely incoherent for pairs of points belonging to different angular positions. By using the coherent-mode structure of propagation invariant fields, the analytical expression of the propagated cross-spectral density, representing fields with radial coherence, is derived. It is shown that beams of this type can be generated in a Fourier transforming optical system. An important feature of the synthesized beams is their ability of being invariant under propagation. The behaviour of the degree of coherence is analysed in terms of the eigenvalues of the modal structure. A numerical ensemble of realizations, at both planes of the considered system, was generated. From this ensemble, the spectral intensity of the proposed beams was obtained. The numerical results show a well-defined principal thin ring of maximum intensity followed by secondary concentric rings, in complete agreement with theoretical predictions. We believe that presented scheme can trigger new research routes in the synthesis of fields with structured coherence.

Neural network surrogate for flow prediction and robust optimization in fractured reservoir systems

Embedded discrete fracture models are widely used to model flow in naturally fractured systems. These models are, however, time-consuming to simulate, and this limits their use for computationally demanding applications such as optimization. In this work we present a deep-learning-based surrogate model for fast prediction of time-varying well flow rates over multiple fracture realizations, for given well bottom-hole pressure schedules. Our surrogate model applies convolutional and recurrent neural networks. The convolutional neural network is used to capture the spatial variability of fractures in different realizations, though the direct input of the fracture geometry is not feasible because structured data are required. We show, however, that the use of the single-phase steady-state pressure solution defined on the structured rock-matrix grid, for each realization, provides the requisite input to the convolutional neural network. The resulting proxy is shown to give accurate flow rate predictions for different discrete fracture realizations. The proxy is then applied for robust optimization (expected net present value computed over an ensemble of realizations is optimized) subject to nonlinear output constraints. Proxy-based optimization provides an 18% improvement in net present value, with an overall speedup of ∼500 relative to simulation-based optimization. The optimized solutions are validated through comparison to simulation results, and agreement is within 1%.

A Practical Approach to Select Representative Deterministic Models Using Multiobjective Optimization from an Integrated Uncertainty Quantification Workflow

Summary Selecting a set of deterministic (e.g., P10, P50, and P90) models is an important and difficult step in any uncertainty quantification workflow. In this paper, we propose to use multiobjective optimization to find a reasonable balance between the often conflicting features that must be captured by these models. We embed this approach into a streamlined uncertainty quantification workflow that seamlessly integrates multirealization history matching, production forecasting with uncertainty ranges, and representative deterministic model selection. Some uncertain parameters strongly impact simulated responses representing historic (production) data and are selected as active parameters for history matching, whereas others are important only for forecasting. An ensemble of conditional realizations of active history-matching parameters is generated in the multirealization history-matching stage using a distributed optimizer that is integrated with either a randomized maximum likelihood (RML) or a Gaussian mixture model (GMM). This ensemble is extended with unconditional realizations of forecast parameters generated by sampling from their prior distribution. Next, the petroleum engineer must select primary and secondary key performance indicators and identify models from this ensemble that optimally generate P10, P50, and P90 values for these indicators. In addition to matching target values of these key performance indicators (e.g., cumulative oil/gas/water production and recovery factor), selected representative models (RMs) typically must satisfy regulatory or management-imposed requirements or constraints (e.g., the value of some key parameters must be within a user-specified tight range). It can be quite difficult to find a set of RMs that satisfy all requirements. Even more challenging, some requirements may conflict with others, such that no single model can satisfy all requirements. To overcome these technical difficulties, we propose in this paper to formulate different requirements and constraints as objectives and develop a novel two-stage multiobjective optimization strategy to find a set of Pareto optimal solutions based on the concept of dominance. In the first stage, we propose selecting P10, P50, and P90 candidates by minimizing the indicator mismatch function and constraints violation function. In the second stage, we propose selecting combinations of P10, P50, and P90 candidates from the previously generated posterior ensemble, obtained in the first stage by optimizing other objectives. One or more sets of RMs can then be selected from the set of optimal solutions according to case-dependent preferences or requirements. Because the number of P10, P50, and P90 candidates selected in the first stage is much smaller than the number of all samples, the proposed two-stage approach performs much more efficiently than directly applying the traditional multiobjective optimization approach or clustering-based approaches. The proposed method is tested and validated against a realistic example. Our results confirm that the proposed method is robust and efficient and finds acceptable solutions with no or minimal violations of constraints. These results suggest that our advanced multiobjective optimization technique can select high-quality RMs by striking a balance between conflicting constraints. Thus, a better decision can be made while running much fewer simulations than would be required with traditional methods.

A Pattern Classification Distribution Method for Geostatistical Modeling Evaluation and Uncertainty Quantification

Geological models are essential components in various applications. To generate reliable realizations, the geostatistical method focuses on reproducing spatial structures from training images (TIs). Moreover, uncertainty plays an important role in Earth systems. It is beneficial for creating an ensemble of stochastic realizations with high diversity. In this work, we applied a pattern classification distribution (PCD) method to quantitatively evaluate geostatistical modeling. First, we proposed a correlation-driven template method to capture geological patterns. According to the spatial dependency of the TI, region growing and elbow-point detection were launched to create an adaptive template. Second, a combination of clustering and classification was suggested to characterize geological realizations. Aiming at simplifying parameter specification, the program employed hierarchical clustering and decision tree to categorize geological structures. Third, we designed a stacking framework to develop the multi-grid analysis. The contribution of each grid was calculated based on the morphological characteristics of TI. Our program was extensively examined by a channel model, a 2D nonstationary flume system, 2D subglacial bed topographic models in Antarctica, and 3D sandstone models. We activated various geostatistical programs to produce realizations. The experimental results indicated that PCD is capable of addressing multiple geological categories, continuous variables, and high-dimensional structures.

Effect of errors on the directional characteristics of a phased antenna array with an arbitrary arrangement of elements

Currently, various types of antenna arrays (AA) are widely used in radio navigation, radar and telecommunication systems. They have a number of advantages related to the possibilities of electronic control of their characteristics and adaptation to signal-interference conditions compared to single emitters. To create the required shape of the radiation pattern, as well as the orientation of its maximum in space, it is necessary to send signals of a certain amplitude and phase to the AA elements, so to form an appropriate amplitude-phase distribution (APD). The error in setting the APD, along with errors in the alignment and determination of the position of the phase centers of individual emitters, have a significant impact on the parameters and characteristics of the AA. Errors in the installation of elements on the canvas of the AA and the deviation of their power supply from the calculated APD lead to a decrease in characteristics, which can be assessed by three criteria: a decrease in directivity (antenna gain); an increase in the level of the side lobes; a change in the accuracy of the installation and the shape of the main beam. An analytical expression for calculating the error can be obtained only for cases of an ordered arrangement of AA elements. The article presents the results of the analysis of the influence of technological errors on the directional characteristics of an AA with an arbitrary arrangement of antenna elements. Statistical averaging of an ensemble of realizations obtained by performing multiple calculations with random sets of parameters is used for the analysis. The laws of probability distribution can be any. The results of calculations for uniformly distributed errors are given as an example.

Comparison of bicoherence on the ensemble of realizations and a selective evaluation of the bispectrum of the dynamics of dangerous parameters of the gas medium during fire

The object of the study is the bicoherence of the bispectrum assessment of the dynamics of dangerous parameters of the gas environment during the ignition of materials. The subject is a measure of bicoherence of the bispectrum estimation from the ensemble of realizations and selective bispectrum estimation for the dynamics of hazardous parameters of the gas environment. The practical importance of the research is the use of the measure of bicoherence of the bispectrum for the early detection of fires. The measure of bicoherence of the dynamics of hazardous parameters of the gas environment is substantiated, which allows them to be numerically compared for the studied bispectrum estimates. As such measure, it is proposed to use the integral value of bicoherence for a given frequency interval, which makes it possible to numerically compare the bicoherence of bispectrum estimates for arbitrary time intervals of the dynamics of hazardous parameters of the gas environment. On the basis of the proposed measure for the frequency range of 0.2–2 Hz, a comparison of the integral bicoherence of the bispectrum estimates was made. The numerical value of the measure was determined for three fixed time intervals of the dynamics of hazardous parameters of the environment, corresponding to the absence of ignition, the occurrence of ignition, and the subsequent burning of test materials in the laboratory chamber. According to the results of the comparison of such values, it was established that the bicoherence of the bispectrum estimation from the ensemble of realizations is the most appropriate for detecting fires. When ignited, the numerical value of the measure for all test materials is about 90°. This means that the nature of the dynamics of hazardous environmental parameters in the event of fires becomes random. In this regard, the proposed measure is recommended to be used as a test for early detection of fires.

Assessing uncertainty in hydrological projections arising from local-scale internal variability of climate

Hydrological impact assessments are increasingly performed at fine spatial and temporal resolutions in order to resolve local-scale changes under a future climate. Apart from the uncertainty represented by different climate models, emission scenarios and post-processing methods, the local-scale internal variability of the climate can be a major source of uncertainty for hydrological projections. To assess the latter at the catchment scale, this paper presents a methodology which is particularly suitable for spatially distributed hydrological models. An ensemble of daily precipitation and daily mean temperature realizations on a high-resolution grid is simulated from stochastic weather generators (WGs) trained on historical data and equipped with climate change information obtained from a regional climate model. Based on the resulting simulated daily runoff data, the significance of changes in the runoff regime is assessed using a statistical hypothesis test, and the variability contributed by the two input variables is quantified using the analysis of variance (ANOVA). As a proof of concept, simulations on a 1-km grid over a period of 19 years are carried out for nine catchments in central Norway. Significant changes in runoff regimes are found, indicating that the trends introduced in the WGs are not overwhelmed by the local-scale internal variability. Variability in the runoff simulations varies substantially throughout the year; it is highest in periods with potential snowmelt and lowest during winter. Temperature is the dominant source of variability in the colder months (November–March) due to its influence on rainfall and snowmelt. High variability in May–June is contributed comparably by both temperature and precipitation. In summer and early autumn the runoff variability is precipitation dominated. The results are in line with findings in the literature where the runoff variability is driven by the large-scale internal climate variability. This indicates that ignoring the local-scale internal variability may yield an underestimation of the overall variability in runoff projections and projected changes.