Stochastic Realization Research Articles

Simulating the Landau-Zener sweep in deeply sub-Ohmic environments.

With the goal to study dissipative Landau-Zener (LZ) sweeps in realistic solid-state qubits, we utilize novel methods from non-Markovian open quantum system dynamics that enable reliable long-time simulations for sub-Ohmic environments. In particular, we combine a novel representation of the dynamical propagator, the uniform time evolving matrix product operator method, with a stochastic realization of finite temperature fluctuations. The latter greatly reduces the computational cost for the matrix product operator approach, enabling convergence in the experimentally relevant deeply sub-Ohmic regime. Our method allows the exact simulation of dynamical protocols with long operation times, such as the LZ sweep, in challenging parameter regimes that are realized in current experimental platforms.

Timing and Likelihood of the Origin of Life Derived from Post-Impact Highly Reducing Atmospheres.

Big impacts on the early Earth would have created highly reducing atmospheres that generated molecules needed for the origin of life, such as nitriles. However, such impactors could have been followed by collisions that were sufficiently big to vaporize the ocean and destroy any pre-existing life. Thus, a post-impact-reducing atmosphere that gives rise to life needs to be followed by a lack of subsequent sterilizing impacts for life to persist. We assume that prebiotic chemistry required a post-impact-reducing atmosphere. Then, using statistics for the impact history on Earth and the minimum impact mass needed to generate post-impact highly reducing atmospheres, we show that the median timing of impact-driven biopoiesis is favored early in the Hadean, ∼4.35 Ga. However, uncertainties are large because impact bombardment is stochastic, and so biopoiesis could have occurred between 4.45 and 3.9 Ga within 95% uncertainty. In an optimistic scenario for biopoiesis from post-impact-reducing atmospheres, we find that the origin of life is favorable in ∼90% of stochastic impact realizations. In our most pessimistic case, biopoiesis is still fairly likely (∼20% chance). This potentially bodes well for life on rocky exoplanets that have experienced an early episode of impact bombardment given how planets form.

Multivariate Geostatistics for Mapping of Transmissivity and Uncertainty in Karst Aquifers

Due to their complex morphology, karst terrains are particularly more fragile and vulnerable to environmental damage compared to most natural systems. Their hydraulic properties, such as their transmissivity (T) and spatial variability, can be relevant for understanding groundwater flow and, consequently, for the sustainable management of water resources. The application of geostatistical methods allows for spatial interpolation and mapping based on observations combined with uncertainty quantification. Direct measurements of T are typically scarce, while those of the specific capacity (Sc) are more frequent. We established a linear and spatial relationship between the logarithms of T and Sc measured in 174 wells in a semi-arid karst region in northeastern Brazil. These relationships were used to construct a cross-variogram, whose Linear Model of Coregionalization proved valid. The values and the cross-variogram of logT and logSc were used to generate interpolations over 2554 values of logSc, which did not spatially coincide with logT. We used ordinary co-kriging (CO-OK) and conditional sequential Gaussian co-simulation (CO-SGS) to generate the interpolations. The cross-variogram of logT and logSc, when considering 174 wells, was isotropic with an exponential structure, a nugget effect of approximately 20% of the sill, and a range of 5 km. Cross-validation indicated an optimal number of 10 neighboring wells used in CO-OK, and we used 500 stochastic realizations in CO-SGS, which were then used to generate maps of logT estimates, deviations derived from the interpolations, and probabilistic scenarios. The resulting transmissivity maps are relevant for the design of groundwater management strategies, including stochastic approaches where the transmissivity realizations can be used to parameterize multiple executions of numerical flow models.

A multiparameter simulation-driven analysis of ship response when turning concerning a required number of irregular wave realizations

The growing implementation of Decision Support Systems on modern ships, digital-twin technology, and the introduction of autonomous vessels cause the marine industry to seek accurate modeling of vessel response. Despite the contemporary 6DOF models can be used to predict ship motions in irregular waves, the impact of their stochastic realization is usually neglected and remains under-investigated. Especially in the case of turning, differences arising from the stochastic representation of the waves may result in excessive ship motions or even stability failure during maneuver execution. Therefore, in this study, statistical distributions of maximum amplitudes of roll, pitch, and lateral acceleration calculated in two representative locations on board a passenger vessel were analyzed concerning stochastic wave realization and existing extremes. The research utilized 6DOF simulation data and numerous realizations of the irregular wave with random phases of its components. Furthermore, the required number of wave realizations allowing for capturing the actual ranges of ship response at an assumed confidence level has been determined and analyzed. Ultimately, the results were compared in the safety-critical cases concerning various wave and operational conditions. The outcome of this study may be found useful by all parties involved in developing maritime autonomous systems and modeling ship motions.

Influence of sedimentary architecture on static connectivity and geothermal doublet performance (Mezőberény, SE Hungary)

Although the Pannonian Basin in Hungary boasts significant geothermal potential, most geothermal wells in the region suffer from reinjection issues. The aim of this study is to examine the impact of the sedimentary architecture of a paralic lacustrine succession on the static connectivity of a geothermal aquifer. This problem was examined for a case-study geothermal doublet drilled in Mezőberény, southeast Hungary, which experienced injectivity problems shortly after commencing operations in 2012, ultimately leading to shut-in of the wells. A characterization of the architecture of the deltaic aquifer has been undertaken through a novel workflow that combines sedimentological and sequence stratigraphic analysis of the well-doublet and stochastic 3D modelling techniques to assess the likely static connectivity between the production and injection wells. Planform dimension of aquifer-forming mouth-bar elements and fluvial channel bodies were estimated from geological analogues, selected based on the thickness values of such sedimentary bodies interpreted on the gamma-ray logs of the well doublet and nearby hydrocarbon wells. In total five mouth-bar and two fluvial channel input geometry groups were selected, and fifty object-based realizations were constructed to analyse the static connectivity of different geological scenarios. The internal lithology of mouth-bar and fluvial-channel elements were modelled by sequential indicator simulations (ten realizations). Results of connected volume analysis indicate that the sandstone content of the aquifer is located within vertically segmented fluvial-channel and mouth-bar elements separated by mud-prone prodelta and lower delta-front deposits. This architectural configuration, in combination with low net-sandstone content suggests limited connectivity between the wells. Across the set of stochastic realizations, the volume of sandstone connecting the injection and production wells is ∼4% of the total aquifer volume, on average. Results of this study shows that simplified reservoir models can lead to over-estimation of connectivity of geothermal doublets. The proposed workflow combines sedimentological analysis and 3D modelling supported by geological analogues to predict sandstone reservoir connectivity of deltaic geothermal reservoirs. The described workflow can be carried out in target areas using existing boreholes to assist borehole planning.

Uncertainty quantification in the Henry problem using the multilevel Monte Carlo method

We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain Henry saltwater intrusion problem. Unknown porosity, permeability and recharge parameters are modelled by using random fields. The classical deterministic Henry problem is non-linear and time-dependent, and can easily take several hours of computing time. Uncertain settings require the solution of multiple realisations of the deterministic problem, and the total computational cost increases drastically. Instead of computing of hundreds random realisations, typically the mean value and the variance are computed. The standard methods such as the Monte Carlo or surrogate-based methods are a good choice, but they compute all stochastic realisations on the same, often, very fine mesh. They also do not balance the stochastic and discretisation errors. These facts motivated us to apply the MLMC method. We demonstrate that by solving the Henry problem on multi-level spatial and temporal meshes, the MLMC method reduces the overall computational and storage costs. To reduce the computing cost further, parallelization is performed in both physical and stochastic spaces. To solve each deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion.

Stochastic analysis of plant available water estimates and soil water balance components simulated by a hydrological model

AbstractThe uncertainty in soil hydraulic parameters is often not taken into account in process‐based hydrological modeling. Performing runs with 104 stochastic parameter realizations, we evaluated the propagation of uncertainty in the Van Genuchten–Mualem (VGM) parameters into estimates of the threshold values of soil water content used to calculate the total and readily available water, and on the long‐term (30 years) simulations of evaporation, transpiration, bottom flux, and runoff by the SWAP hydrological model. The simulated scenarios included weather data from a location in southeast Brazil and seven soils from the same region cropped with maize, comprising a wide range of texture classes. The results showed that uncertainties in VGM parameters affect the estimates of total and readily available water. Water balance components obtained by a deterministic simulation with average VGM parameters did not always agree with the average or median of stochastic simulations, and stochastic simulations including parameter uncertainties should be preferred. Variations in yearly rainfall characteristics were more important for bottom flux and evaporation, while transpiration and runoff were more strongly influenced by the variations in soil hydraulic properties.

Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

Multi-reservoir system response to alternative stochastically simulated stationary hydrologic scenarios: An evaluation for the Apalachicola-Chattahoochee-Flint (ACF) Basin

Study regionApalachicola-Chattahoochee-Flint (ACF) Basin in the Southeast US Study focusOperational rules of managed river systems are typically developed based on historical hydrology. This approach fails to consider alternative plausible hydrologic conditions that may occur outside the observational period-of-record. Here, we evaluated operational rules of a transboundary managed river system—the ACF Basin—with multiple reservoirs under historical observations and 100 stochastic streamflow realizations representing the current streamflow conditions of the basin. These scenarios, which had comparable averages as the historical records but greater extremes, were simulated by coupling a stochastic streamflow model with a basin-wide river system model. We used these scenarios to evaluate the response of the ACF Basin against metrics for urban water supply, required freshwater inflows, floodplain forest ecosystem water needs and hydropower generation. The evaluation was done based on the magnitude, frequency, duration and seasonality of these metrics. New hydrological insight of the regionThe unique aspect of this paper is using a stochastic streamflow model coupled with a river basin model to evaluate the response of the ACF Basin’s current operational rules under several hypothetical plausible stationary hydrologic scenarios. We found that, overall, the basin response in terms of all the metrics used here was less favorable under the alternative stationary hydrologic scenarios than the historical hydrology. Our evaluations suggested that the reservoir operational rules should be revisited to consider a broader range of plausible hydrologic conditions.

Integrated Geomodel Accuracy Enhancement Based on Embedded MPS Geological Modeling for Thin Interbedded Reservoirs

Continental delta deposits are characterized by strong heterogeneity in the lateral direction; meanwhile, reservoir development is challenged by rapid changes in rock properties. Thus, it is critical to use proper methods for fine characterization to confirm the distributions of thin interbedded reservoirs. The aim of this study was to propose a novel workflow for integrated research on the 3D geomodeling of thin interbedded reservoirs, using the Triassic T2a1 formation in the Tahe Oilfield B9 area of the Tarim Basin as a case study. The complicated representation of thin interbeds in a 3D geomodel was simulated using a multiscale joint controlling strategy, based on wells (Points), 2D geological cross-sections (Lines), and horizontal wells (Surfaces). The resistivity inversion results from the horizontal wells validated the proof of the plane distribution of the thin interbeds within the drilled area, and this quantitative statistic provided effective parameters and guidance for 3D interbed geomodeling. In this study, comprehensive 3D facies modeling was divided into 3D interbed geomodeling and 3D sedimentary facies modeling. An optimized interbed geomodel was picked out from multiple stochastic simulation realizations, and the drilled horizontal well data were used to constrain the simulation process, so the simulation results were more consistent with the real distribution of the thin interbed morphology. Classical two-point geostatistical methods, the multipoint simulation (MPS) geostatistical method, and the hierarchical mindset were integrated for the microfacies simulation. This procedure demonstrated a good ability to characterize thin interbed reservoirs in continental delta deposits. An MPS training image obtained from a high-resolution satellite photo was used to fix the issue of the relationships between the distributions and configurations of all microfacies within the spatial distribution. A 3D lithofacies interbed model was embedded into the 3D facies model. This comprehensive facies model served as a constraint condition in the property modeling process. A porosity model was simulated using separate stratigraphy and individual microfacies controls, as facies-controlled property modeling has been used as a prior foundation for field development planning in the Tahe Oilfield B9 case. The porosity model was then used as a basis for permeability modeling, and a water saturation model was created using the J function and all of the constraints from the other two property models. Finally, all the results were validated using dynamic production data from the Tahe Oilfield B9 wells, with good matching observed between the geological models. There was only a 0.92% difference in reservoir volume between the reservoir simulation results and the static geological model results using our solution.

Sampling Gaussian stationary random fields: A stochastic realization approach

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the difficulty of being computationally expensive, which is even more serious when the dimension of the random field is large. This paper proposes an efficient stochastic realization approach for sampling Gaussian stationary random fields from a systems and control point of view. Specifically, we take the exponential and squared exponential covariance functions as examples and make a decoupling assumption when there are multiple dimensions. Then a rational spectral density is constructed in each dimension using techniques from covariance extension, and the corresponding autoregressive moving-average (ARMA) model is obtained via spectral factorization. As a result, samples of the random field with a specific covariance function can be generated very efficiently in the space domain by implementing the ARMA recursion using a Gaussian white noise input. Such a procedure is computationally cheap due to the fact that the constructed ARMA model has a low order. Furthermore, the same method is integrated to multiscale simulations where interpolations of the generated samples are achieved when one zooms into finer scales. Both theoretical analysis and simulation results show that our approach performs favorably compared with covariance matrix decomposition methods.

Solving the stochastic dynamics of population growth.

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters.

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.

Stochastic wind farm flow generation using a reduced order model of LES

Large eddy simulations are computationally expensive, which typically limits the simulation time and hence the statistics useful for validation. Here, a reduced order model with a stochastic engine is used to generate stochastic inflow to 48 wind turbines in the Lillgrund wind farm. The stochastic flow realization captures the power production and more importantly the correct cross-correlations in power and blade root flapwise bending moments over the large spatiotemporal region, which the wind farm covers. The analysis show how the cross-correlation increase further into the wind farm, where the highly turbulent flow becomes increasingly self-organized and how the dynamic interaction across the entire wind farm is captured by the first eight modes. Overall, the reduced order model captures the correct dynamics at a fraction of the computational cost, effectively generalizing the LES results beyond a relatively short simulation period.

StochHyProp: A software to generate stochastic realizations of correlated parameters dedicated to soil hydraulic properties

StochHyProp is a software to generate stochastic parameter realizations based on mean parameter values, standard errors, and correlation matrix by the application of Cholesky decomposition, specially dedicated to soil hydraulic parameters. The produced parameter realizations can be used in stochastic modelling to yield frequency distributions of hydrological model outputs. The software reads the input parameters, performs the internal calculation procedure, and generates output files containing the requested number of parameter realizations. Special features include the generation of merged parameter properties, the exclusion of outlying values, and the reading of statistics from other software frequently used to fit soil hydraulic parameters.

Diffusion with stochastic resetting screened by a semipermeable interface

In this paper we consider the diffusive search for a bounded target with its boundary totally absorbing. We assume that the target is surrounded by a semipermeable interface given by the closed surface with . That is, the interface totally surrounds the target and thus partially screens the diffusive search process. We also assume that the position of the diffusing particle (searcher) randomly resets to its initial position x 0 according to a Poisson process with a resetting rate r. The location x 0 is taken to be outside the interface, , which means that resetting does not occur when the particle is within the interior of . (Otherwise, the particle would have to cross the interface in order to reset to x 0.) Hence, the semipermeable interface also screens out the effects of resetting. We illustrate the theory by explicitly solving the boundary value problem for a three-dimensional (3D) spherically symmetric interface and a concentric spherical target. We calculate the mean first passage time (MFPT) to find (be absorbed by) the target and explore its behavior as a function of the permeability κ 0 of the interface and the radius of the interface R. In particular, we find that increasing R for a fixed target size reduces the MFPT and increases the optimal resetting rate at which the MFPT is minimized. We also find that the sensitivity of the MFPT to changes in κ 0 is a decreasing function of R. Finally, we introduce a stochastic single-particle realization of the search process based on a generalization of so-called snapping out Brownian motion (BM). The latter sews together successive rounds of reflecting BM on either side of the interface. The main challenge is establishing that the probability density generated by the snapping out BM satisfies the permeable boundary conditions at the interface. We show how this can be achieved using renewal theory.

A Hybrid Embedded Discrete Fracture Model and Dual-Porosity, Dual-Permeability Workflow for Hierarchical Treatment of Fractures in Practical Field Studies

Summary Natural fracture systems comprise numerous small features and relatively few large ones. At field scale, it is impractical to treat all fractures explicitly. We represent the largest fractures using an embedded discrete fracture model (EDFM) and account for smaller ones using a dual-porosity, dual-permeability (DPDK) idealized representation of the fracture network. The hybrid EDFM + DPDK approach uses consistent discretization schemes and efficiently simulates realistic field cases. Further speedup can be obtained using aggregation-based upscaling. Capabilities to visualize and post-process simulation results facilitate understanding for effective management of fractured reservoirs. The proposed approach embeds large discrete fractures as EDFM within a DPDK grid (which contains both matrix and idealized fracture continua for smaller fractures) and captures all connections among the triple media. In contrast with existing EDFM formulations, we account for discrete fracture spacing within each matrix cell via a new matrix-fracture transfer term and use consistent assumptions for classical EDFM and DPDK calculations. In addition, the workflow enables coarse EDFM representations using flow-based cell-aggregation upscaling for computational efficiency. Using a synthetic case, we show that the proposed EDFM + DPDK approach provides a close match of simulation results from a reference model that represents all fractures explicitly, while providing runtime speedup. It is also more accurate than previous standard EDFM and DPDK models. We demonstrate that the matrix-fracture transfer function agrees with flow-based upscaling of high-resolution fracture models. Next, the automated workflow is applied to a waterflooding study for a giant carbonate reservoir, with an ensemble of stochastic fracture realizations. The overall workflow provides the computational efficiency needed for performance forecasts in practical field studies, and the 3D visualization allows for the derivation of insights into recovery mechanisms. Finally, we apply a finite-volume tracer-based flux post-processing scheme on simulation results to analyze production allocation and sweep for understanding expected waterflood performance.

Wind-induced fragility of a monopole structure via Artificial Neural Network based surrogate analysis

Although brute-force Monte Carlo (BFMC) sampling has been commonly used in performance-based wind engineering (PBWE) due to its robustness and efficiency, the computing cost required by the considerable amounts of repetitious, stochastic realizations for situations that involve large structures and a multitude of uncertainties is still prohibitive. To alleviate the computational burden, this communication proposes a surrogate modeling approach, based on artificial neural networks (ANNs), to evaluate the probabilistic integral required to quantify wind-induced fragilities. The resultant ANN models form a computationally viable alternative between input and output variables, based on a database of observations obtained through BFMC stochastic simulations. A preliminary study is conducted to examine the fragility of a slender, monopole tower structure under the excitation of multidirectional, mixed-climate wind loads. The ANN-powered surrogate results show adequate accuracy while drastically reducing the computing time to less than 1% of the cost of BFMC approach. It is promising to incorporate the surrogate ANN modeling in a PBWE framework.

Estimating porosity distribution of a heterogeneous alluvial aquifer by GPU-accelerated 3D conditional stochastic inversion of common-offset GPR reflection data

Three-dimensional (3D) high-resolution and accurate characterization of the heterogeneity in an alluvial aquifer is critical to predicting the groundwater flow and contaminant transport. In this study, we extend the previous 2D conditional stochastic inversion method with respect to common-offset ground-penetrating radar (GPR) data to 3D for the estimation of 3D porosity distribution in a heterogeneous alluvial aquifer. First, 3D stochastic realizations of subsurface properties can be obtained using the fast Fourier transform moving average (FFT-MA) method, and the realizations are conditioned to borehole porosity measurements available in the 3D survey area, as well as to the geostatistical parameters derived from the borehole logs and the processed 3D GPR data. Next, the realizations are constantly modified and regenerated via a localized simulated annealing optimization strategy, which ultimately makes their corresponding synthetic data offer an acceptable fit to the GPR data. To accelerate the computational speed of 3D inversion, we design and implement the multi-GPUs multi-node parallelization of the 3D conditional stochastic inversion algorithm. The proposed 3D inversion algorithm is positively verified through the application to field GPR data collected at the Boise Hydrogeophysical Research Site near Boise, Idaho, USA. Our results indicate that the proposed 3D inversion method has the potential to effectively recover the fine-scale porosity distribution of a heterogeneous alluvial aquifer.

Prediction of numerical homogenization using deep learning for the Richards equation

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and frequently calculate macroscopic parameters. More specifically, we train neural networks with a training set consisting of stochastic permeability realizations and corresponding computed macroscopic targets (effective permeability tensor, homogenized stiffness matrix, and right-hand side vector). Our proposed deep learning scheme develops nonlinear maps between such permeability fields and macroscopic characteristics, and the treatment for Richards equation’s nonlinearity is included in the predicted coarse-scale homogenized stiffness matrix, which is a novelty. This strategy’s good performance is demonstrated by several numerical tests in two-dimensional model problems, for predictions of the macroscopic properties and consequently solutions.