Browsing by Author "Mohammadi, Farid"

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Open Access
Bayesian Model Selection for hydro-morphodynamic models
(2017) Mohammadi, Farid
A good grasp of hydro-morphodynamic processes plays a major role in modern river management to accommodate its often-conflicting functions. In the last century, a variety of models has been developed to improve our perception of sediment transport and the resulting changes in river bed topography, using several empirical formulations. Therefore, there is a demonstrated need to establish a framework that helps the river engineer to select the closest model to the measurements. This study suggested a Bayesian Model Selection (BMS) framework to direct the modeler towards the most robust and sensible representation of the hydro-morphodynamic conditions of the river under investigation. The proposed framework employs Bayesian Model Evidence (BME) resulting from Bayesian Model Averaging (BMA) as a model evaluation yardstick for ranking competing models. BMA performs a compromise between bias and variance, i.e. it blends a measure for goodness of fit with a penalty for unacceptable model complexity. This approach requires many model simulations, which are computationally expensive. However, this issue can be diminished by a mathematically optimal response surface via the aPC technique projects the original model. This response surface, also known as a reduced (surrogate) model can exhibit the reliance of the model on all relevant parameters for calibration at high order accuracy. The proposed framework was implemented in the model selection of two test cases; namely a test case model, based on an experiment done by Yen and Lee (1995) and a river model of a 10-km stretch of the lower Rhine, provided by the FederalWaterways Research Institute (BAW) in Karlsruhe. The results demonstrated that the proposed framework was acceptably able to detect the most desirable model in which a good agreement existed between the simulation results and measurement data when the complete knowledge of initial parameters lacked. Further, the BMS framework could direct us to the most probable parameter regions for the task of optimization via probability density distributions of uncertain variables. Overall, this research fills a void in the literature with respect to the selection of sediment transport equation for representation of hydro-morphodynamics of natural rivers. The suggested approach provides an objective guidance in the model selection to assist even less experienced users by reducing the professional expertise required for further optimization tasks.
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 Bayesian framework for uncertainty-aware validation benchmarks
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2023) Mohammadi, Farid; Flemisch, Bernd (apl. Prof. Dr. rer. nat.)
Over the last century, computational modeling in geoscience, especially in porous media research, has witnessed tremendous improvement. After decades of development, the state-of-the-art simulators can now solve coupled partial differential equations governing the complex subsurface multiphase flow system within a practically large spatial and temporal domain. Given the importance of computational modeling, quality assessment of these models in light of the purpose of a given simulation is of paramount importance to engineering designers and managers, public officials, and those affected by the decisions based on the predictions. Users and developers of computational simulations deal with a challenging question: How should confidence in modeling and simulation be critically assessed? Validation is one of the primary methods for building and quantifying confidence in modeling and simulation. It investigates the degree to which a model accurately represents reality from the perspective of the intended application of the model. Usually, this comparison between model outputs and experimental data constitutes plotting the model results against data on the same axes to provide a visual assessment of agreement or lack thereof. While comparisons between model and data are at the heart of any validation procedure, there are several concerns with such naive comparisons. First, these comparisons tend to provide qualitative rather than quantitative assessments and are clearly insufficient as a basis for making decisions regarding model validity. Second, naive comparisons often disregard or only partly account for existing uncertainties in the experimental observations or the model input parameters. Third, such comparisons can not reveal whether the model is appropriate for the intended purposes, as they mainly focus on the agreement in the observable quantities. These pitfalls give rise to the need for an uncertainty-aware framework that includes a validation metric. This metric shall provide a measure for comparison of the system response quantities of an experiment with the ones from a computational model while accounting for uncertainties in both in a rigorous way. To address this need, we developed a statistical framework incorporating a probabilistic modeling technique using a fully Bayesian approach. The dissertation aims to help modelers perform uncertainty aware model validation benchmarks. A two-stage Bayesian multi-model framework is discussed for modeling tasks where a set of models are at hand. To make this framework applicable for computationally demanding models, it is extended to a surrogate-assisted framework, keeping the computational costs at a reasonable level. Moreover, correction factors were introduced to compensate for the surrogate error in the Bayesian hypothesis testing and Bayesian model selection, as using surrogate representations instead of the full-fidelity computational models introduces additional errors to the validation metrics. In this dissertation, I show how the Bayesian formalism could be materialized by employing the concept of polynomial chaos expansion to achieve more accurate surrogates with a sparse representation and account for the uncertainty in the surrogate’s predictions. I also highlight how such surrogate models could be constructed with as few simulations as the computational budget allows. To this end, sequential adaptive sampling strategies are discussed, in which one attempts to augment the initial design iteratively. By doing so, informative regions in the parameter space are adequately explored. These regions are more likely to provide valuable information on the behavior of the original model responses. Using a sequential sampling strategy avoids the waste of computational resources, as opposed to the so-called one-shot designs. A series of benchmark studies are conducted to investigate the predictive capabilities of different sparsity and sequential adaptive sampling methods. Moreover, I introduce BayesValidRox, an open-source, object-oriented Python package that provides an automated workflow for surrogate-based sensitivity analysis, Bayesian calibration, and validation of computational models with a modular structure. The uncertainty-aware validation framework was applied to a range of cases in the field of subsurface hydro-system modeling, mainly to flow and transport in porous media, such as flow simulation models in fractured porous media, coupling free flow and porous medium flow, and microbially induced calcite precipitation. However, this validation framework can be transferred to other disciplines in which models are used for prediction.
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
Thermochemical heat storage in a lab-scale indirectly operated CaO/Ca(OH)2 reactor - numerical modeling and model validation through inverse parameter estimation
(2021) Seitz, Gabriele; Mohammadi, Farid; Class, Holger
Calcium oxide/Calcium hydroxide can be utilized as a reaction system for thermochemical heat storage. It features a high storage capacity, is cheap, and does not involve major environmental concerns. Operationally, different fixed-bed reactor concepts can be distinguished; direct reactor are characterized by gas flow through the reactive bulk material, while in indirect reactors, the heat-carrying gas flow is separated from the bulk material. This study puts a focus on the indirectly operated fixed-bed reactor setup. The fluxes of the reaction fluid and the heat-carrying flow are decoupled in order to overcome limitations due to heat conduction in the reactive bulk material. The fixed bed represents a porous medium where Darcy-type flow conditions can be assumed. Here, a numerical model for such a reactor concept is presented, which has been implemented in the software DuMux. An attempt to calibrate and validate it with experimental results from the literature is discussed in detail. This allows for the identification of a deficient insulation of the experimental setup. Accordingly, heat-loss mechanisms are included in the model. However, it can be shown that heat losses alone are not sufficient to explain the experimental results. It is evident that another effect plays a role here. Using Bayesian inference, this effect is identified as the reaction rate decreasing with progressing conversion of reactive material. The calibrated model reveals that more heat is lost over the reactor surface than transported in the heat transfer channel, which causes a considerable speed-up of the discharge reaction. An observed deceleration of the reaction rate at progressed conversion is attributed to the presence of agglomerates of the bulk material in the fixed bed. This retardation is represented phenomenologically by modifying the reaction kinetics. After the calibration, the model is validated with a second set of experimental results. To speed up the calculations for the calibration, the numerical model is replaced by a surrogate model based on Polynomial Chaos Expansion and Principal Component Analysis.