Browsing by Author "Oladyshkin, Sergey"

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Open Access
Bayesian calibration and validation of a large‐scale and time‐demanding sediment transport model
(2020) Beckers, Felix; Heredia, Andrés; Noack, Markus; Nowak, Wolfgang; Wieprecht, Silke; Oladyshkin, Sergey
This study suggests a stochastic Bayesian approach for calibrating and validating morphodynamic sediment transport models and for quantifying parametric uncertainties in order to alleviate limitations of conventional (manual, deterministic) calibration procedures. The applicability of our method is shown for a large‐scale (11.0 km) and time‐demanding (9.14 hr for the period 2002-2013) 2‐D morphodynamic sediment transport model of the Lower River Salzach and for three most sensitive input parameters (critical Shields parameter, grain roughness, and grain size distribution). Since Bayesian methods require a significant number of simulation runs, this work proposes to construct a surrogate model, here with the arbitrary polynomial chaos technique. The surrogate model is constructed from a limited set of runs (n=20) of the full complex sediment transport model. Then, Monte Carlo‐based techniques for Bayesian calibration are used with the surrogate model (105 realizations in 4 hr). The results demonstrate that following Bayesian principles and iterative Bayesian updating of the surrogate model (10 iterations) enables to identify the most probable ranges of the three calibration parameters. Model verification based on the maximum a posteriori parameter combination indicates that the surrogate model accurately replicates the morphodynamic behavior of the sediment transport model for both calibration (RMSE = 0.31 m) and validation (RMSE = 0.42 m). Furthermore, it is shown that the surrogate model is highly effective in lowering the total computational time for Bayesian calibration, validation, and uncertainty analysis. As a whole, this provides more realistic calibration and validation of morphodynamic sediment transport models with quantified uncertainty in less time compared to conventional calibration procedures.
Open Access
Bayesian calibration points to misconceptions in three‐dimensional hydrodynamic reservoir modeling
(2023) Schwindt, Sebastian; Callau Medrano, Sergio; Mouris, Kilian; Beckers, Felix; Haun, Stefan; Nowak, Wolfgang; Wieprecht, Silke; Oladyshkin, Sergey
Three‐dimensional (3d) numerical models are state‐of‐the‐art for investigating complex hydrodynamic flow patterns in reservoirs and lakes. Such full‐complexity models are computationally demanding and their calibration is challenging regarding time, subjective decision‐making, and measurement data availability. In addition, physically unrealistic model assumptions or combinations of calibration parameters may remain undetected and lead to overfitting. In this study, we investigate if and how so‐called Bayesian calibration aids in characterizing faulty model setups driven by measurement data and calibration parameter combinations. Bayesian calibration builds on recent developments in machine learning and uses a Gaussian process emulator as a surrogate model, which runs considerably faster than a 3d numerical model. We Bayesian‐calibrate a Delft3D‐FLOW model of a pump‐storage reservoir as a function of the background horizontal eddy viscosity and diffusivity, and initial water temperature profile. We consider three scenarios with varying degrees of faulty assumptions and different uses of flow velocity and water temperature measurements. One of the scenarios forces completely unrealistic, rapid lake stratification and still yields similarly good calibration accuracy as more correct scenarios regarding global statistics, such as the root‐mean‐square error. An uncertainty assessment resulting from the Bayesian calibration indicates that the completely unrealistic scenario forces fast lake stratification through highly uncertain mixing‐related model parameters. Thus, Bayesian calibration describes the quality of calibration and correctness of model assumptions through geometric characteristics of posterior distributions. For instance, most likely calibration parameter values (posterior distribution maxima) at the calibration range limit or with widespread uncertainty characterize poor model assumptions and calibration.
Open Access
Efficient modeling of environmental systems in the face of complexity and uncertainty
(2014) Oladyshkin, Sergey; Helmig, Rainer (Prof. Dr.-Ing.)
Strong industrial development of the last century has led to a significant increase in public demand for different types of energy and, as a consequence, to an enormous increase in demand for natural resources. Naturally, all types of nature resources form a part of our surrounding environment. In order to extract natural resources a wide variety of technologies has been developed. This has led to a strong rise in interventions in the environment continuing up to the present days. At the same time, environmental systems form one of the largest and most important classes of complex dynamic systems. For this reason, society needs a better understanding of the environment in order to have an efficient and safe interaction for the sake of maximized welfare and sustainability in resources management. In particular, the ability to predict how the environment changes over time or how it will react to planned interventions is indispensable. However our surroundings behave non-trivially in various time and spatial scales. Moreover, many environmental systems are heterogeneous, non-linear and dominated by real-time influences of external driving forces. Unfortunately, a complete picture of environmental systems is not available, because many of these systems cannot be observed directly and only can be derived using sparse measurements. Moreover, environmental data is hardly available and expensive to acquire. Overall, this leads to limited observability, and an inherent uncertainty in all modeling endeavors. Still, research over several decades has showed that modeling plays a very important role in reconstructing (as far as possible) the complete and complex picture of the environment systems and offers a unique way to predict behavior of such multifaceted systems. The current thesis contains research in the field of environmental modeling in the face of complexity and uncertainty. The presented thesis is divided into three parts and refers to diverse applications such as underground petroleum reservoirs, groundwater flow, radioactive waste deposits and storage of energy relevant gases. Part 1 focuses on physical concepts and offers several possibilities to accelerate the modeling process. Part 2 deals with efficient model reduction methodologies for uncertainty quantification. Part 3 demonstrates application to the storage of energy relevant gases in geological formations and discusses related challenges.
Open Access
Gaussian active learning on multi-resolution arbitrary polynomial chaos emulator : concept for bias correction, assessment of surrogate reliability and its application to the carbon dioxide benchmark
(2023) Kohlhaas, Rebecca; Kröker, Ilja; Oladyshkin, Sergey; Nowak, Wolfgang
Surrogate models are widely used to improve the computational efficiency in various geophysical simulation problems by reducing the number of model runs. Conventional one-layer surrogate representations are based on global (e.g. polynomial chaos expansion, PCE) or on local kernels (e.g., Gaussian process emulator, GPE). Global representations omit some details, while local kernels require more model runs. The existing multi-resolution PCE is a promising hybrid: it is a global representation with local refinement. However, it can not (yet) estimate the uncertainty of the resulting surrogate, which techniques like the GPE can do. We propose to join multi-resolution PCE and GPE s into a joint surrogate framework to get the best out of both worlds. By doing so, we correct the surrogate bias and assess the remaining uncertainty of the surrogate itself. The resulting multi-resolution emulator offers a pathway for several active learning strategies to improve the surrogate at acceptable computational costs, compared to the existing PCE-kriging approach it adds the multi-resolution aspect. We analyze the performance of a multi-resolution emulator and a plain GPE using didactic test cases and a CO2 benchmark, that is representative of many alike problems in the geosciences. Both approaches show similar improvements during the active learning, but our multi-resolution emulator leads to much more stable results than the GPE. Overall, our suggested emulator can be seen as a generalization of multi-resolution PCE and GPE concepts that offers the possibility for active learning.
Open Access
Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems
(2023) Kröker, Ilja; Oladyshkin, Sergey; Rybak, Iryna
Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes-Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy’s law in the porous-medium domain and the classical interface conditions across the fluid–porous interface including the conservation of mass, the balance of normal forces and the Beavers–Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers-Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indices on the aMR-PC expansion and conduct the corresponding numerical simulations.
Open Access
Improving thermochemical energy storage dynamics forecast with physics-inspired neural network architecture
(2020) Praditia, Timothy; Walser, Thilo; Oladyshkin, Sergey; Nowak, Wolfgang
Thermochemical Energy Storage (TCES), specifically the calcium oxide (CaO)/calcium hydroxide (Ca(OH)2) system is a promising energy storage technology with relatively high energy density and low cost. However, the existing models available to predict the system's internal states are computationally expensive. An accurate and real-time capable model is therefore still required to improve its operational control. In this work, we implement a Physics-Informed Neural Network (PINN) to predict the dynamics of the TCES internal state. Our proposed framework addresses three physical aspects to build the PINN: (1) we choose a Nonlinear Autoregressive Network with Exogeneous Inputs (NARX) with deeper recurrence to address the nonlinear latency; (2) we train the network in closed-loop to capture the long-term dynamics; and (3) we incorporate physical regularisation during its training, calculated based on discretized mole and energy balance equations. To train the network, we perform numerical simulations on an ensemble of system parameters to obtain synthetic data. Even though the suggested approach provides results with the error of 3.96 x 10^(-4) which is in the same range as the result without physical regularisation, it is superior compared to conventional Artificial Neural Network (ANN) strategies because it ensures physical plausibility of the predictions, even in a highly dynamic and nonlinear problem. Consequently, the suggested PINN can be further developed for more complicated analysis of the TCES system.
Open Access
Information‐theoretic scores for Bayesian model selection and similarity analysis : concept and application to a groundwater problem
(2023) Morales Oreamuno, Maria Fernanda; Oladyshkin, Sergey; Nowak, Wolfgang
Bayesian model selection (BMS) and Bayesian model justifiability analysis (BMJ) provide a statistically rigorous framework for comparing competing models through the use of Bayesian model evidence (BME). However, a BME-based analysis has two main limitations: (a) it does not account for a model's posterior predictive performance after using the data for calibration and (b) it leads to biased results when comparing models that use different subsets of the observations for calibration. To address these limitations, we propose augmenting BMS and BMJ analyses with additional information-theoretic measures: expected log-predictive density (ELPD), relative entropy (RE) and information entropy (IE). Exploring the connection between Bayesian inference and information theory, we explicitly link BME and ELPD together with RE and IE to highlight the information flow in BMS and BMJ analyses. We show how to compute and interpret these scores alongside BME, and apply the framework to a controlled 2D groundwater setup featuring five models, one of which uses a subset of the data for calibration. Our results show how the information-theoretic scores complement BME by providing a more complete picture concerning the Bayesian updating process. Additionally, we demonstrate how both RE and IE can be used to objectively compare models that feature different data sets for calibration. Overall, the introduced Bayesian information-theoretic framework can lead to a better-informed decision by incorporating a model's post-calibration predictive performance, by allowing to work with different subsets of the data and by considering the usefulness of the data in the Bayesian updating process.
Open Access
Learning groundwater contaminant diffusion‐sorption processes with a finite volume neural network
(2022) Praditia, Timothy; Karlbauer, Matthias; Otte, Sebastian; Oladyshkin, Sergey; Butz, Martin V.; Nowak, Wolfgang
Improved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.
Open Access
Stability criteria for Bayesian calibration of reservoir sedimentation models
(2023) Mouris, Kilian; Acuna Espinoza, Eduardo; Schwindt, Sebastian; Mohammadi, Farid; Haun, Stefan; Wieprecht, Silke; Oladyshkin, Sergey
Modeling reservoir sedimentation is particularly challenging due to the simultaneous simulation of shallow shores, tributary deltas, and deep waters. The shallow upstream parts of reservoirs, where deltaic avulsion and erosion processes occur, compete with the validity of modeling assumptions used to simulate the deposition of fine sediments in deep waters. We investigate how complex numerical models can be calibrated to accurately predict reservoir sedimentation in the presence of competing model simplifications and identify the importance of calibration parameters for prioritization in measurement campaigns. This study applies Bayesian calibration, a supervised learning technique using surrogate-assisted Bayesian inversion with a Gaussian Process Emulator to calibrate a two-dimensional (2d) hydro-morphodynamic model for simulating sedimentation processes in a reservoir in Albania. Four calibration parameters were fitted to obtain the statistically best possible simulation of bed level changes between 2016 and 2019 through two differently constraining data scenarios. One scenario included measurements from the entire upstream half of the reservoir. Another scenario only included measurements in the geospatially valid range of the numerical model. Model accuracy parameters, Bayesian model evidence, and the variability of the four calibration parameters indicate that Bayesian calibration only converges toward physically meaningful parameter combinations when the calibration nodes are in the valid range of the numerical model. The Bayesian approach also allowed for a comparison of multiple parameters and found that the dry bulk density of the deposited sediments is the most important factor for calibration.
Open Access
A surrogate-assisted uncertainty-aware Bayesian validation framework and its application to coupling free flow and porous-medium flow
(2023) Mohammadi, Farid; Eggenweiler, Elissa; Flemisch, Bernd; Oladyshkin, Sergey; Rybak, Iryna; Schneider, Martin; Weishaupt, Kilian
Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid-porous interface. These models include a porous-medium model using Darcy’s law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems’ behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model’s predictive capabilities, and make a probabilistic model comparison.
Open Access
Surrogate-based Bayesian comparison of computationally expensive models : application to microbially induced calcite precipitation
(2021) Scheurer, Stefania; Schäfer Rodrigues Silva, Aline; Mohammadi, Farid; Hommel, Johannes; Oladyshkin, Sergey; Flemisch, Bernd; Nowak, Wolfgang
Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. The considered models differ in the underlying hypotheses about the process structure. Once observation data become available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest to perform both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we will use the arbitrary polynomial chaos expansion. Considering that surrogate representations are only approximations of the analyzed original models, we account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian model justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.
Open Access
Uncertainties and robustness with regard to the safety of a repository for high-level radioactive waste : introduction of a research initiative
(2024) Kurgyis, Kata; Achtziger-Zupančič, Peter; Bjorge, Merle; Boxberg, Marc S.; Broggi, Matteo; Buchwald, Jörg; Ernst, Oliver G.; Flügge, Judith; Ganopolski, Andrey; Graf, Thomas; Kortenbruck, Philipp; Kowalski, Julia; Kreye, Phillip; Kukla, Peter; Mayr, Sibylle; Miro, Shorash; Nagel, Thomas; Nowak, Wolfgang; Oladyshkin, Sergey; Renz, Alexander; Rienäcker-Burschil, Julia; Röhlig, Klaus-Jürgen; Sträter, Oliver; Thiedau, Jan; Wagner, Florian; Wellmann, Florian; Wengler, Marc; Wolf, Jens; Rühaak, Wolfram
The Federal Company for Radioactive Waste Disposal (BGE mbH) is tasked with the selection of a site for a high-level radioactive waste repository in Germany in accordance with the Repository Site Selection Act. In September 2020, 90 areas with favorable geological conditions were identified as part of step 1 in phase 1 of the Site Selection Act. Representative preliminary safety analyses are to be carried out next to support decisions on the question, which siting regions should undergo surface-based exploration. These safety analyses are supported by numerical simulations building on geoscientific and technical data. The models that are taken into account are associated with various sources of uncertainties. Addressing these uncertainties and the robustness of the decisions pertaining to sites and design choices is a central component of the site selection process. In that context, important research objectives are associated with the question of how uncertainty should be treated through the various data collection, modeling and decision-making processes of the site selection procedure, and how the robustness of the repository system should be improved. BGE, therefore, established an interdisciplinary research cluster to identify open questions and to address the gaps in knowledge in six complementary research projects. In this paper, we introduce the overall purpose and the five thematic groups that constitute this research cluster. We discuss the specific questions addressed as well as the proposed methodologies in the context of the challenges of the site selection process in Germany. Finally, some conclusions are drawn on the potential benefits of a large method-centered research cluster in terms of simulation data management.