Parameter Uncertainty Quantification Research Articles

Rational Kriging

This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimator of the mean from rational kriging is much more well behaved than that of ordinary kriging. Parameter estimation and uncertainty quantification for rational kriging are proposed using a Gaussian process framework. A generalized version of rational kriging is also proposed, which includes ordinary and rational kriging as special cases. Extensive simulations carried out over a wide class of functions show that the generalized rational kriging performs on par or better than both ordinary and rational kriging in terms of prediction and uncertainty quantification. The only extra step needed for generalized rational kriging over ordinary kriging is the computation of Perron eigenvector of an augmented correlation matrix which can be computed in near linear time and therefore, its overall computational complexity is no more than that of ordinary kriging. The potential applications of the new kriging methods in the emulation of computationally expensive models and model calibration problems are illustrated with real and simulated examples. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

A U-Net architecture as a surrogate model combined with a geostatistical spectral algorithm for transient groundwater flow inverse problems

Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems.

Evolving Improved Sampling Protocols for Dose–Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3–20), and it reduced the parameter variance metric by 33–37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Uncertainty Quantification of Engineering Parameters for a Nuclear Reactor Loaded with Dispersed Fuel Particles

Owing to their high intrinsic safety, dispersed fuel particles are an important fuel pattern for fourth-generation nuclear reactors. Due to the unique cladding layers and the random dispersion characteristics, dispersed fuel particles significantly differ from pressurized water reactors regarding operation-induced uncertainty. This study quantitatively analyzed overall uncertainty while considering a random distribution of dispersed fuel particles, material thickness, and fuel enrichment. The results demonstrated that, for all packing fractions, the uncertainty induced by the random dispersion of dispersed fuel particles was below 0.03%. For every packing fraction, the differences between the results obtained by the regular and the random distribution models increased, and then decreased, until reaching its maximum (1.297%) at 15%. Keff decreased as the radius of the UO2 kernel increased; Keff increased as the thickness of the cladding layer increased; the uncertainty of Keff was 1.003% when a random distribution of particles, material thickness, and fuel enrichment were taken into consideration; the uncertainty of the power distribution of reactor core assemblies was maximized (1.495%) at the edge of the reactor core. Quantitative analysis of uncertainty provides references for the optimization of design and safety margin analysis for reactors.

Efficient spin-up of Earth System Models using sequence acceleration.

Marine and terrestrial biogeochemical models are key components of the Earth System Models (ESMs) used to project future environmental changes. However, their slow adjustment time also hinders effective use of ESMs because of the enormous computational resources required to integrate them to a pre-industrial equilibrium. Here, a solution to this "spin-up" problem based on "sequence acceleration", is shown to accelerate equilibration of state-of-the-art marine biogeochemical models by over an order of magnitude. The technique can be applied in a "black box" fashion to existing models. Even under the challenging spin-up protocols used for Intergovernmental Panel on Climate Change (IPCC) simulations, this algorithm is 5 times faster. Preliminary results suggest that terrestrial models can be similarly accelerated, enabling a quantification of major parametric uncertainties in ESMs, improved estimates of metrics such as climate sensitivity, and higher model resolution than currently feasible.

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.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Bayesian finite element model updating techniques have found widespread application in the structural health monitoring. The conventional Bayesian modeling framework (CBMF) identifies the posterior distribution of structural parameters using data from a single experiment. However, structural parameters exhibit variability due to changes in environmental or experimental conditions, an aspect overlooked by CBMF. In recent years, the hierarchical Bayesian modeling framework (HBMF) has gradually attracted attention. This framework incorporates an additional layer of hyperparameters and utilizes multiple sets of experimental data to describe the variability in structural parameters caused by changes in experimental conditions. Unfortunately, the increase in hyperparameters and data size leads the HBMF to face the dilemma of exceedingly high computational costs. To address this issue, this study proposes an improved hierarchical Bayesian modeling framework (IHBMF). To enhance the computational efficiency of IHBMF, the importance sampling method is employed to simplify the computation of the likelihood function for hyperparameters. Subsequently, a surrogate model based on arbitrary polynomial chaos expansion is introduced to further reduce the computational cost of IHBMF. The framework's accuracy and efficiency were validated through analysis of a simply supported beam and a steel pedestrian bridge. The results demonstrate that IHBMF not only delivers a more accurate quantification of structural parameter uncertainty than CBMF but also exhibits higher computational efficiency compared to HBMF, showcasing its superior capability in structural health monitoring applications.

Bayesian uncertainty quantification of modal parameters and RRF identification of transmission towers with limited measured vibration data

The resonant response factor (RRF) sensitive to modal parameters, including the damping ratio and frequency, is a critical parameter for wind-resistant design of extra high voltage (EHV) transmission towers, because it directly affects the calculation of the wind vibration coefficient. However, the research on operational modal analysis (OMA) of in-service EHV transmission towers is limited due to the high risk of field monitoring. Therefore, it is critical to determine the size of sufficient data samples or minimum monitoring duration for the OMA of a transmission tower. In this study, an investigation of uncertainty quantification in Bayesian OMA of EHV transmission towers with small data samples from the ambient dynamic test is carried out. The uncertainty of the resonant component factor for wind-resistance design is proposed and quantified, which could provide engineering designers with a reference for confidence levels. Firstly, a field test system is installed on a multipurpose EHV transmission tower with a closed-loop cat head and a pair of cross-arms, to gather the acceleration responses. Then, the OMA for the transmission tower is carried out by the fast Bayesian FFT (FBFFT) method to determine the modal parameters as well as the associated posterior uncertainty. The small sample analysis of OMA for the transmission tower is further performed to obtain sufficient data samples and minimum monitoring duration. Finally, the distribution of the RRF is presented with the different confidential levels. It is found that a sampling length of 600 s could fulfill the basic needs of accuracy in Bayesian OMA and the determination of RRF. The outcomes of this study may provide a reference for the wind-resistance design parameter selection of the similar type of transmission towers.

Bi-Level Inverse Robust Optimization Dispatch of Wind Power and Pumped Storage Hydropower Complementary Systems

This paper presents a bi-level inverse robust economic dispatch optimization model consisting of wind turbines and pumped storage hydropower (PSH). The inner level model aims to minimize the total generation cost, while the outer level introduces the optimal inverse robust index (OIRI) for wind power output based on the ideal perturbation constraints of the objective function. The OIRI represents the maximum distance by which decision variables in the non-dominated frontier can be perturbed. Compared to traditional methods for quantifying the worst-case sensitivity region using polygons and ellipses, the OIRI can more accurately quantify parameter uncertainty. We integrate the grid multi-objective bacterial colony chemotaxis algorithm and the bisection method to solve the proposed model. The former is adopted to solve the inner level problem, while the latter is used to calculate the OIRI. The proposed approach establishes the relationship between the maximum forecast deviation and the minimum generation cost associated with each non-dominated solution in the optimal load allocation. To demonstrate its economic viability and effectiveness, we simulate the proposed approach using real power system operation data and conduct a comparative analysis.

A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations

A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations

A bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings

This paper proposes a bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings. Firstly, the stochastic subspace method in combination with the bootstrap technique enables the estimation of multiple sets of modal parameters from raw data series. Then, a bootstrap-based stabilization diagram is used to extract the physical modes. Finally, the modal identification and associated uncertainty quantification results are determined via statistical analysis. Through a numerical study of high-rise buildings, the performance of the proposed method is validated, demonstrating that it can provide reliable modal parameter identification and uncertainty quantification as well as has good noise immunity. Furthermore, the developed approach is employed to identify modal parameters of a 600-m-tall skyscraper during a typhoon, proving its applicability to field measurements and structural health monitoring of high-rise buildings. This paper aims to present a novel tool for modal parameter identification and associated uncertainty quantification of high-rise buildings.

Endothelial cells signaling and patterning under hypoxia: a mechanistic integrative computational model including the Notch-Dll4 pathway.

Introduction: Several signaling pathways are activated during hypoxia to promote angiogenesis, leading to endothelial cell patterning, interaction, and downstream signaling. Understanding the mechanistic signaling differences between endothelial cells under normoxia and hypoxia and their response to different stimuli can guide therapies to modulate angiogenesis. We present a novel mechanistic model of interacting endothelial cells, including the main pathways involved in angiogenesis. Methods: We calibrate and fit the model parameters based on well-established modeling techniques that include structural and practical parameter identifiability, uncertainty quantification, and global sensitivity. Results: Our results indicate that the main pathways involved in patterning tip and stalk endothelial cells under hypoxia differ, and the time under hypoxia interferes with how different stimuli affect patterning. Additionally, our simulations indicate that Notch signaling might regulate vascular permeability and establish different Nitric Oxide release patterns for tip/stalk cells. Following simulations with various stimuli, our model suggests that factors such as time under hypoxia and oxygen availability must be considered for EC pattern control. Discussion: This project provides insights into the signaling and patterning of endothelial cells under various oxygen levels and stimulation by VEGFA and is our first integrative approach toward achieving EC control as a method for improving angiogenesis. Overall, our model provides a computational framework that can be built on to test angiogenesis-related therapies by modulation of different pathways, such as the Notch pathway.

Parameter estimation for reactive chromatography model by Bayesian inference and parallel sequential Monte Carlo

Reactive chromatography overcomes many disadvantages of conventional separation processes by improving yields and reduces costs by combining reaction and separation in a single operation. Model-based optimization is essential to realize industrial applications of this process. Parameters in the model must be estimated accurately, and evaluating the uncertainty of the model parameters is crucial. However, uncertainty quantification of model parameters has not been performed for reactive chromatography processes. In this study, we propose an approach to estimate the parameter uncertainty of reactive chromatography processes using Bayesian inference and parallel sequential Monte Carlo. As an example, the esterification synthesis of acetic acid and methanol catalyzed by a cation exchange resin was considered. Parameter estimation was performed using a reactive chromatography experiment and a non-reactive experiment in which only the products were injected. The results of the analysis showed that using both the reactive and non-reactive chromatography experimental data simultaneously improved the accuracy of the estimation. In addition, correlations between some parameters were revealed.

Copula-based Bayesian uncertainty quantification framework of SST turbulence model for flow over a Gaussian bump

Quantitatively analyze the uncertainties in turbulence models is of great meaning for research and engineering. In this paper, we develop a Bayesian uncertainty analysis framework based on copulas. The proposed framework is applied to the parametric uncertainty quantification and calibration of the shear-stress transport turbulence model for the flow over a Gaussian bump. A copula function is used to establish the correlation between variables and construct the weight function, which enables greater consideration of Bayesian inference. Prior analysis is conducted based on Sobol indices with the nonintrusive polynomial chaos method, demonstrating the important effects of κ, a1, and β∗ on the flow, both for the wall force coefficients and the Reynolds shear stress. Next, the wall force coefficients and Reynolds shear stress are used as training sets to verify the effectiveness of the method. The results show that modeling the relationship based on copulas is necessary and effective, and that the weight function adaptively balances the influence of physical quantities at different inference locations. The proposed method effectively corrects the computational deviations of the corresponding physical quantities. In addition, the confidence interval for the posterior sample is increased, enhancing the likelihood of obtaining results close to the actual values.

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone, surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions (UNEs). However, the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved, including the generation of complex fracture networks, reactivation of natural fractures and faults, and thermo-hydro-mechanical-chemical (THMC) coupling of radionuclide gas transport in the subsurface. In this study, we provide an experimental investigation of hydro-mechanical (HM) coupling among gas flow, stress states, rock deformation, and rock damage using a unique multi-physics triaxial direct shear rock testing system. The testing system also features redundant gas pressure and flow rate measurements, well suited for parameter uncertainty quantification. Using porous tuff and tight granite samples that are relevant to historic UNE tests, we measured the Biot effective stress coefficient, rock matrix gas permeability, and fracture gas permeability at a range of pore pressure and stress conditions. The Biot effective stress coefficient varies from 0.69 to 1 for the tuff, whose porosity averages 35.3% ± 0.7%, while this coefficient varies from 0.51 to 0.78 for the tight granite (porosity <1%, perhaps an underestimate). Matrix gas permeability is strongly correlated to effective stress for the granite, but not for the porous tuff. Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event: (1) The porous tuff shows apparent fracture dilation or compression upon stress changes, which does not necessarily change the gas permeability; (2) The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement; and (3) Hydromechanical coupling among stress states, rock damage, and gas flow appears to be stronger in tight granite than in porous tuff.

Combining formal methods and Bayesian approach for inferring discrete-state stochastic models from steady-state data

Stochastic population models are widely used to model phenomena in different areas such as cyber-physical systems, chemical kinetics, collective animal behaviour, and beyond. Quantitative analysis of stochastic population models easily becomes challenging due to the combinatorial number of possible states of the population. Moreover, while the modeller easily hypothesises the mechanistic aspects of the model, the quantitative parameters associated to these mechanistic transitions are difficult or impossible to measure directly. In this paper, we investigate how formal verification methods can aid parameter inference for population discrete-time Markov chains in a scenario where only a limited sample of population-level data measurements—sample distributions among terminal states—are available. We first discuss the parameter identifiability and uncertainty quantification in this setup, as well as how the existing techniques of formal parameter synthesis and Bayesian inference apply. Then, we propose and implement four different methods, three of which incorporate formal parameter synthesis as a pre-computation step. We empirically evaluate the performance of the proposed methods over four representative case studies. We find that our proposed methods incorporating formal parameter synthesis as a pre-computation step allow us to significantly enhance the accuracy, precision, and scalability of inference. Specifically, in the case of unidentifiable parameters, we accurately capture the subspace of parameters which is data-compliant at a desired confidence level.

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver. Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations and in vivo data of a patient suffering from hepatic tumor lesions. Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% for k trans, 22% ± 6% for v e and 89% ± 5% for v p than the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For the in vivo data, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p < 0.0001). Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

Implementation of Asynchronous Distributed Gauss-Newton Optimization Algorithms for Uncertainty Quantification by Conditioning to Production Data

Summary Previous implementation of the distributed Gauss-Newton (DGN) optimization algorithm ran multiple optimization threads in parallel, employing a synchronous running mode (S-DGN). As a result, it waits for all simulations submitted in each iteration to complete, which may significantly degrade performance because a few simulations may run much longer than others, especially for time-consuming real-field cases. To overcome this limitation and thus improve the DGN optimizer’s execution, we propose two asynchronous DGN (A-DGN) optimization algorithms in this paper. The two A-DGN optimization algorithms are (1) the local-search algorithm (A-DGN-LS) to locate multiple maximum a-posteriori (MAP) estimates and (2) the integrated global-search algorithm with the randomized maximum likelihood (RML) method (A-DGN + RML) to generate hundreds of RML samples in parallel for uncertainty quantification. We propose using batch together with a checking time interval to control the optimization process. The A-DGN optimizers check the status of all running simulations after every checking time frame. The iteration index of each optimization thread is updated dynamically according to its simulation status. Thus, different optimization threads may have different iteration indices in the same batch. A new simulation case is proposed immediately once the simulation of an optimization thread is completed, without waiting for the completion of other simulations. We modified the training data set updating algorithm using each thread’s dynamically updated iteration index to implement the asynchronous running mode. We apply the modified QR decomposition method to estimate the sensitivity matrix at the best solution of each optimization thread by linear interpolation of all or a subset of the training data to avoid the issue of solving a linear system with a singular matrix because of insufficient training data points in early batches. A new simulation case (or search point) is generated by solving the Gauss-Newton (GN) trust-region subproblem (GNTRS) using the estimated sensitivity matrix. We developed a more efficient and robust GNTRS solver using eigenvalue decomposition (EVD). The proposed A-DGN optimization methods are tested and validated on a 2D analytical toy problem and a synthetic history-matching problem and then applied to a real-field deepwater reservoir model. Numerical tests confirm that the proposed A-DGN optimization methods can converge to solutions with matching quality comparable to those obtained by the S-DGN optimizers, saving on the time required for the optimizer to converge by a factor ranging from 1.3 to 2 when compared to the S-DGN optimizer depending on the problem. The new A-DGN optimization algorithms improve efficiency and robustness in solving history-matching or inversion problems, especially for uncertainty quantification of subsurface model parameters and production forecasts of real-field reservoirs by conditioning production data.

Uncertainty Quantification for the Noah‐MP Land Surface Model: A Case Study in a Grassland and Sandy Soil Region

AbstractLand surface models rely on a multitude of parameters to simulate land‐atmosphere interactions, but the parameter uncertainty can limit the reliability of model predictions. This study utilizes a parameter uncertainty quantification (UQ) framework to quantify and reduce the parameter uncertainty of the Noah‐MP land surface model in a grassland and sandy soil region in the Midwest of the USA. First, the sparse polynomial chaos expansion method which can quantify the interaction effect of parameters, is employed. A relatively small parameter sample size (i.e., 20 times of the number of parameters) was sufficient to identify the sensitive parameters; an additional sensitive parameter, the saturated soil hydraulic conductivity, was screened out compared to previous study. Then, based on the selected sensitive parameters, the weighted multi‐objective adaptive surrogate modeling‐based optimization algorithm is used as the parameter optimization method. The optimization results showed that the root mean square error of flux of latent heat (FLH) on about 82% of the total grids was reduced, and the number was about 57% for gross primary production (GPP) compared to the results using the original parameter settings, indicating that the Pareto parameter set by the UQ framework improved the Noah‐MP model in simulating FLH and GPP in a grassland and sandy soil region in the Midwest of the USA.

Bayesian estimation of parameters and uncertainty of a 3-D dipping fault using gravity anomalies

SUMMARY Many significant geophysical anomalies are generated by fault systems, and effectively estimating fault parameters is a key step to understand the characteristics of these field sources. In general, the 2-D dipping fault is frequently utilized to simplify the representation of fault geometry. However, this approach could lead to larger errors when comparing realistic scenarios with simplifications. In this study, we use a parametrized 3-D dipping model to represent fault systems and compute gravity anomalies using an analytic method in the wavenumber domain. To estimate the marginal distribution of the 3-D dipping fault parameters, we utilize the Bayesian theory that integrates the likelihood function and prior information. Subsequently, we use the Markov chain Monte Carlo sampling method to assess the marginal distribution of the parameters. Compared with other deterministic inversion approaches, our method provides an effective means of quantifying parameter uncertainty. We first use synthetic data to validate the effectiveness of the proposed method. The results demonstrate the efficiency of our method in revealing 3-D dipping fault parameters and evaluating their uncertainty. We subsequently apply our method to the Pudu River fault, located in Yunnan Province, China, to demonstrate its practical applicability. Two alternative realistic fault models referred the prior seismic profile have been proposed. The optimal parameters and uncertainty with the specific model have been estimated. The results show that the fault characteristics retrieved by our method deviate slightly from existing knowledge. Specifically, the estimated depth of the bottom surface is greater than that reported in previous studies. This could potentially offer us new perspectives on the geological evolution and structural attributes of this fault.