Model Calibration Algorithm Research Articles

Anticipated Wait and Its Effects on Consumer Choice, Pricing, and Assortment Management

Problem definition: We investigate the effects of waiting time, mainly due to production in a make-to-batch-order (MTBO) system, on consumer choice behavior, pricing, assortment, and model estimation. In an MTBO system, the seller/manufacturer first collects orders placed within a certain period of time into a batch and then starts the production process. After the production of all orders in a batch are complete, the products are then shipped and delivered to individual consumers. Because of batch production and shipping, the disutility of the waiting time exhibits negative externality. Methodology/results: We adopt the widely used multinomial logit (MNL) model as a starting point and incorporate the anticipated wait into consumers’ decision making. The derived model, referred to as the MNL with wait model, is a solution of the rational expectation equilibrium and is capable of capturing the effects of negative externality induced by anticipated wait that may change the substitution patterns dramatically. We characterize the multiproduct price optimization problem under the MNL with wait model by establishing a one-to-one mapping between the price vector and the choice probability vector. We find that firms tend to charge higher prices for time-consuming items and charge lower prices for time-saving items compared with the optimal prices under the standard MNL model. In addition to price competition, we also study the Cournot-type competition, in which the decision is the choice probability for each firm and establish the existence of a Nash equilibrium. For assortment optimization, we identify mild conditions under which the optimality of revenue-ordered assortments still holds. However, the assortment problem under the MNL with wait model is generally NP-hard, so we develop approximation algorithms with performance guarantees and provide an easy-to-compute tight upper bound. Moreover, we develop an efficient maximum likelihood-based algorithm for model calibration and further conduct numerical studies to showcase the importance of incorporating disutility due to wait in estimation, pricing, and assortment planning problems. Managerial implications: The MNL with wait model can increase prediction accuracy for consumers’ choice behavior especially when they are aware of the potential wait. Failure to take into account the effects of anticipated wait in firms’ decision making may lead to substantial losses. Funding: The research of C. Ke is supported in part by the National Natural Science Foundation of China [Grant 72101113]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2020.0346 .

Velocity model calibration for surface microseismic monitoring based on a 3D gently inclined layered equivalent model

Abstract Shale gas has become a major source of natural gas production and has received worldwide attention. Hydraulic fracturing is widely performed to stimulate oil and gas wells with considerable success. Given high-precision microseismic (MS) event locations, we can predict the development trend and region of fracturing and evaluate the stimulation effect, thereby providing technical guidance for subsequent exploitation. An accurate velocity model is essential for MS event positioning. However, simple velocity models, such as the uniform or vertical transverse isotropy (VTI) velocity model, are generally applied to calibrate the velocity model. Despite calibration, the VTI model may still face challenges in obtaining accurate MS event locations. Based on the structural characteristics of shale, we propose a novel local velocity model calibration algorithm for surface MS monitoring. To calibrate the velocity model, the actual strata interfaces are replaced with 3D gently inclined planes. We use very fast simulated annealing to concurrently tune the velocity, depth, and angle parameters of the model. Through the assessment of both the stacked amplitude at the position of the perforation shot and the relocation error of the perforation shot, we determine the ideal velocity model. To evaluate the effectiveness of our approach, we conduct experiments on both a synthetic model and a field dataset, and statistically analyze the location error. The results show that the proposed method obviously reduces the perforation shot relocation error and is well-suited for calibrating velocity models that are close to slightly inhomogeneous layered media.

Gradient-based optimization for multi-scale geographically weighted regression

Multi-scale geographically weighted regression (MGWR) is among the most popular methods to analyze non-stationary spatial relationships. However, the current model calibration algorithm is computationally intensive: its runtime has a cubic growth with the sample size, while its memory use grows quadratically. We propose calibrating MGWR with gradient-based optimization. This is obtained by analytically deriving the gradient vector and the Hessian matrix of the corrected Akaike information criterion (AICc) and wrapping them with a trust-region optimization algorithm. We evaluate the model quality empirically. Our method converges to the same coefficients and produces the same inference as the current method but it has a substantial computational gain when the sample size is large. It reduces the runtime to quadratic convergence and makes the memory use linear with respect to sample size. Our new algorithm outperforms the existing alternatives and makes MGWR feasible for large spatial datasets.

Modelling parametric uncertainty in large-scale stratigraphic simulations

We combine forward stratigraphic models with a suite of uncertainty quantification and stochastic model calibration algorithms for the characterization of sedimentary successions in large scale systems. The analysis focuses on the information value provided by a probabilistic approach in the modelling of large-scale sedimentary basins. Stratigraphic forward models (SFMs) require a large number of input parameters usually affected by uncertainty. Thus, model calibration requires considerable time both in terms of human and computational resources, an issue currently limiting the applications of SFMs. Our work tackles this issue through the combination of sensitivity analysis, model reduction techniques and machine learning-based optimization algorithms. We first employ a two-step parameter screening procedure to identify relevant parameters and their assumed probability distributions. After selecting a restricted set of important parameters these are calibrated against available information, i.e., the depth of interpreted stratigraphic surfaces. Because of the large costs associated with SFM simulations, probability distributions of model parameters and outputs are obtained through a data driven reduced complexity model. Our study demonstrates the numerical approaches by considering a portion of the Porcupine Basin, Ireland. Results of the analysis are postprocessed to assess (i) the uncertainty and practical identifiability of model parameters given a set of observations, (ii) spatial distribution of lithologies. We analyse here the occurrences of sand bodies pinching against the continental slope, these systems likely resulting from gravity driven processes in deep sea environment.

Land subsidence caused by seasonal groundwater level fluctuations in Kawajima (Japan) and one-dimensional numerical modeling with an evolutionary algorithm

The causes of land subsidence in Kawajima, Japan, have been investigated through data compilation and numerical modeling. Land subsidence has progressed despite a gradual increase in the hydraulic head in the long term. Taking into account the temporal changes and depth distribution of groundwater abstractions, the contraction of formations, and the complexity of the hydrogeological structures, it is proposed that agricultural groundwater use is one of the main triggers for land subsidence. A one-dimensional numerical simulator for coupled groundwater flow and soil deformation was developed with an evolutionary algorithm for model calibration. The calculated spatiotemporal changes in the past-maximum effective stress showed that plastic consolidation in the clayey layers progressed part by part every summer season resulting in long-term and gradual land subsidence under the same range of groundwater level fluctuations. The results also showed that the plastic deformation occurred in both the Holocene and Pleistocene sediments in the drought years, leading to significant subsidence. The model’s predictive performance showed good potential except for a structural prediction error after the Tohoku Earthquake in 2011. The scenario analysis indicated that management of the groundwater level in summer is one of the effective countermeasures in suppressing land subsidence caused by seasonal groundwater level fluctuations. These methodologies and findings can be used for groundwater management in similar cases around the world. Additional investigation is necessary on the influence of large earthquakes in deformation conditions in order to further improve the developed model.

Singular Value Decomposition and Quasi-Moment-Method as pathloss model calibration alternatives

Using indoor-to-outdoor pathloss measurements for a femtocell network, this paper presents a comparative evaluation of the performances of Singular Value Decomposition (SVD) and Quasi-Moment-Method (QMM) as pathloss model calibration tools. First, the performances of two published SVD models are compared with those of corresponding QMM models, developed through the calibration of basic ECC33 and WINNER II models. Then, and after noting that the ‘base models’ from which the poorer performing, published SVD calibrations reportedly derive, are either incompletely described or characterized by misprints, alternative ‘base models’ are prescribed by this paper. It is then shown through analysis that QMM and SVD represent alternative implementations of the same basic model calibration algorithm. Computational results due to the alternative models suggest that better performance metrics (Mean Prediction Error (MPE) and Root Mean Square Prediction Error (RMSPE)) are recorded, when existing basic models are modified to mimic the SVD ‘base model’, prior to SVD/QMM calibration. Indeed, because the MPE due to the calibration of the alternative models are all close to zero (actually equal to zero in a few cases), the associated residual profiles closely follow the Gaussian distribution typically assumed in the literature, for shadow fading modelling.

Research on SDH Model Calibration Algorithm for Robotic Arm Based on Differential Transform

With the development of science and technology, it has had a great impact on the manufacturing industry. The manufacturing industry has higher and higher requirements for industrial manipulators, and the expectations for the quality and function of the industrial manipulators in the manufacturing industry are increasing day by day. At the same time, the requirements for the working accuracy of the manipulators are also getting higher and higher. In this paper, a new method is proposed. An error compensation and calibration algorithm based on parameter separation and integration of the standard DH model (SDH) is used to construct the kinematic model of the manipulator. The six groups of structural parameters of the six-axis manipulator are calibrated once every two groups, thereby eliminating the influence of the singular value of the position of the manipulator. Finally, the feasibility of this scheme is verified by simulation experiments, the accuracy is ensured, and the expected purpose is achieved. Because the method in this paper has high requirements on the posture of the manipulator, it reduces the overall calibration calculation and saves time, which has a certain effect on the improvement of the industrial manipulator in the manufacturing industry.

Herd immunity levels and multi-strain influenza epidemics in Russia: a modelling study

AbstractIn the present paper, we consider a compartmental epidemic model which simulates the co-circulation of three influenza strains, A(H1N1)pdm09, A(H3N2), and B, in a population with the history of exposure to these virus strains. A strain-specific incidence data for the model input was generated using long-term weekly ARI incidence and virologic testing data. The algorithm for model calibration was developed as a combination of simulated annealing and BFGS optimization methods. Two simulations were carried out, assuming the absence and the presence of protected individuals in the population, with 2017– 2018 and 2018–2019 epidemic seasons in Moscow as a case study. It was shown that strain-specific immune levels defined by virologic studies might be used in the model to obtain plausible incidence curves. However, different output parameter values, such as fractions of individuals exposed to particular virus strain in the previous epidemic season, can correspond to similar incidence trajectories, which complicates the assessment of herd immunity levels based on the model calibration. The results of the study will be used in the research of the interplay between the immunity formation dynamics and the circulation of influenza strains in Russian cities.

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

Computer modeling and simulation is fast-moving towards clinical applications to advance cardiac diagnosis and aid treatment planning. As cardiac models become more popular and useful, the need to tailor these models for individual subjects has grown. Therefore, model identification becomes an important step of cardiac modeling. Cardiac model identification is a challenging task, particularly for simulation in high organizational scales such as tissue and organ scales, as the models are nonlinear and involve hidden ion channel gating variables. In this study, we proposed a two-stage model calibration algorithm to estimate the parameters of cardiac tissue model using membrane potential data. Specifically, an ensemble Kalman Filter (EnKF) is used in the first stage to track the membrane potentials and the hidden ion channel gating variables; the outputs from the EnKF are used as the initial values to calculate forward prediction in the second stage. The optimization algorithm minimizes the sum of squared errors in both stages through a coarse and a fine optimization. The proposed method is validated through multiple simulation designs, which shows good accuracy and efficiency.

Hardware Trojan Detection Leveraging a Novel Golden Layout Model Towards Practical Applications

Globalization trend in integrated circuit design and manufacturing process has increased the vulnerability of integrated circuit. These vulnerabilities mainly caused by hardware Trojan have a serious impact on the security of integrated circuits. Although side-channel analysis approach is the most promising Trojan detection approach, nearly all side-channel analysis approaches rely heavily on the availability of golden chips, which are extremely difficult to obtain. In this paper, a golden layout model instead of fabricated golden chips is introduced for the practical application of hardware Trojan detection approaches. The simulated voltage variations generated from the golden layout model at different process corners serve as golden reference, thus fabricated golden chips are not required during detection. Further, silicon measurements are performed to obtain the voltage variations of fabricated chips, and a model calibration algorithm is utilized to calibrate the golden model in the presence of process variations and random noise. Finally, the Trojan detection is formulated as a two-class classification problem, and the Trojan is identified using the partitioning around medoids algorithm. Experimental results demonstrate that the similarities between the simulated traces and measured traces are greater than 98.81%, and the proposed approach distinguishes the Trojan chips correctly even under ± 15% process variation.

History matching of surfactant-polymer flooding using polynomial chaos expansion

This paper proposes a robust framework for history matching which employs a sequential execution of sensitivity analysis, proxy modeling and inverse optimization to determine the optimized parameter space of model parameters. A mechanistic surfactant-polymer (SP) flood model is considered for history matching with an ultimate goal of accurately calibrating models that describe physical subprocesses of surfactant flooding, polymer flooding and displacement process. The employed model calibration algorithm starts with Sobol sensitivity analysis which reduces the large uncertain space of model parameters to determine the most important stochastic variables. The resulting low-dimensional parameter space is then represented via appropriate orthonormal basis of polynomial chaos expansion (PCE-proxy). An inverse optimization problem is then posed that minimizes the miss-fit between PCE-proxy response and experimental observations by employing a Genetic Algorithm. Finally, the epistemic uncertainty in PCE-proxy is quantified by combining it with a Gaussian regression process called Kriging.We use this framework to calibrate the SP flood model by history matching a single coreflood experiment for quantities of interest such as pressure drop profile and cumulative oil recovery curve. We then show that the calibrated model is successfully able to predict all our quantities of interest for two other coreflood experiments without any ad-hoc tuning of parameters. The proposed proxy-accelerated inverse optimization framework shows significant promise for model calibration or to improve the quality of history matched results.

Surrogate based model calibration for pressurized water reactor physics calculations

In this work, a scalable algorithm for model calibration in nuclear engineering applications is presented and tested. The algorithm relies on the construction of surrogate models to replace the original model within the region of interest. These surrogate models can be constructed efficiently via reduced order modeling and subspace analysis. Once constructed, these surrogate models can be used to perform computationally expensive mathematical analyses. This work proposes a surrogate based model calibration algorithm. The proposed algorithm is used to calibrate various neutronics and thermal-hydraulics parameters. The virtual environment for reactor applications-core simulator (VERA-CS) is used to simulate a three-dimensional core depletion problem. The proposed algorithm is then used to construct a reduced order model (a surrogate) which is then used in a Bayesian approach to calibrate the neutronics and thermal-hydraulics parameters. The algorithm is tested and the benefits of data assimilation and calibration are highlighted in an uncertainty quantification study and requantification after the calibration process. Results showed that the proposed algorithm could help to reduce the uncertainty in key reactor attributes based on experimental and operational data.

A Linear Regression Framework for the Verification of Bayesian Model Calibration Algorithms

We describe a framework for the verification of Bayesian model calibration routines. The framework is based on linear regression and can be configured to verify calibration to data with a range of observation error characteristics. The framework is designed for efficient implementation and is suitable for verifying code intended for large-scale problems. We propose an approach for using the framework to verify Markov chain Monte Carlo (MCMC) software by combining it with a nonparametric test for distribution equality based on the energy statistic. Our matlab-based reference implementation of the framework is shown to correctly distinguish between output obtained from correctly and incorrectly implemented MCMC routines. Since correctness of output from an MCMC software depends on choosing settings appropriate for the problem-of-interest, our framework can potentially be used for verifying such settings.

Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.

American option valuation under time changed tempered stable Lévy processes

Abstract Given that the underlying assets in financial markets exhibit stylized facts such as leptokurtosis, asymmetry, clustering properties and heteroskedasticity effect, this paper presents a novel model for pricing American option under the assumptions that the stock price processes are governed by time changed tempered stable Levy process. As this model is constructed by introducing random time changes into tempered stable (TS) processes which specially refer to normal tempered stable (NTS) distribution as well as classical tempered stable (CTS) distribution, it permits infinite jumps as well as capturing random varying time in stochastic volatility, consequently taking into account the empirical facts such as leptokurtosis, skewness and volatility clustering behaviors. We employ the Fourier-cosine technique to calculate American option and propose the improved Particle Swarm optimization (IPSO) intelligent algorithm for model calibration. To demonstrate the advantage of the constructed model, we carry out empirical research on American index option in financial markets across wide ranges of models, with the time changing normal tempered stable distribution model yielding a superior performance than others.

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss–Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models.

Abstract PR12: A model of HGF and EGF dual ligand stimulation in ACHN cells constructed with the aid of a novel model merging heuristic

Abstract The investigation of context-specific perturbations of cell signaling pathways requires the construction of large scale network models of multiple interacting pathways. A key issue in the production of these models is the process of model calibration, sometimes referred to as regression or optimization, during which parameters of a model are systematically adjusted to improve the model's predictions on a set of training data. We have developed a novel heuristic, termed “model merging,” to exploit parameter information from simpler models in the construction of new complex models. Using this merging heuristic, we developed a model of HGF and EGF stimulation of the MAP kinase cascade in ACHN cells, a renal cancer cell line. We constructed the model of HGF and EGF stimulation by first constructing smaller models of stimulation by each separate ligand. We use the single ligand models to inform the training of the dual ligand model by applying the model merging heuristic. Our model accurately reflects the time courses of pMET, pEGFR, and pMAPK under single ligand and dual ligand stimulation over two-hour time courses. It also captures several previously unmodeled features of MET and EGFR pathway crosstalk. The goal of model merging is to resolve parameter differences while maintaining the predictive quality of the previously known models. By the nature of model calibration, there are discrepancies between parameter estimates of the single ligand models whenever a parameter appears in both models. We design a scoring system for model predictions that takes into account the discrepancies between the parameter estimates. To resolve these discrepancies, our model merging heuristic iteratively adjusts the scoring system to create a series of optimization problems. The solutions to the series of problems converge to a resolved parametrization for the general model while maintaining the high quality of predictions of the component models. A key advantage of our heuristic over other model calibration algorithms is its ability to identify context-specific differences in parametrizations during model calibration. This is possible because the heuristic does not enforce any context-specific or context-free assumptions. Rather, it tries to resolve differences between multiple parameter sets by searching for a single consensus parameter set. If the training data precludes such a consensus for some of the parameters, then the heuristic can identify these parameters and simultaneously resolve the other parameters for which there is a consensus. In this way, the heuristic identifies parameters that are context-specific. This major advantage of our model merging method was integral to our construction of a model of HGF and EGF stimulation of the MAP Kinase cascade in ACHN cells. We identify context-specific parameters that describe a previously known, receptor-specific difference in phospho-MAPK negative feedback to the adapter protein GAB1. Identification of context-specific parametrizations also demonstrated that a prior model of EGF stimulated MAP kinase signaling employed an overly simplified mechanism of phospho-MAPK negative feedback to the protein SOS. Using this more detailed mechanism, we are now able to better interrogate the role of MAPK negative feedback in the more general multipathway setting. We also investigated the generalizability of our model merging heuristic by applying it repeatedly to a simplified version of our dual ligand model. We demonstrate that applying model merging in combination with Nelder-Mead calibration generates a significantly more robust estimation of parameters than Nelder-Mead calibration alone. Model merging thus produces a higher likelihood of finding a global best model parametrization instead of a local best parametrization. These results highlight the potential for our model merging technique to enable the creation of multipathway models with high mechanistic detail with reduced computational cost. This proffered talk is also presented as Poster A10. Citation Format: Andrew L. Matteson. A model of HGF and EGF dual ligand stimulation in ACHN cells constructed with the aid of a novel model merging heuristic [abstract]. In: Proceedings of the AACR Special Conference on Chemical Systems Biology: Assembling and Interrogating Computational Models of the Cancer Cell by Chemical Perturbations; 2012 Jun 27-30; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2012;72(13 Suppl):Abstract nr PR12.

Genetic Algorithms for the Optimal Operation of Sprinkle Irrigation Systems under Deterministic Loading Conditions

The paper presents a methodology developed for the optimal management and operation of sprinkle irrigation networks. Some typical problems are presented and solved through Genetic Algorithms (GAs), assuming that the loads (demands) at nodes are cyclic and deterministically established. In particular, an algorithm for model calibration is first introduced, aimed at the minimization of the maximum errors between measured and calculated values. Since the operation of such systems is highly water and energy demanding, two algorithms for controlling pressure and pumps are described: the first is aimed at finding the optimal location and control of a set of devices (pressure reducing valves and/or closed gate valves) in order to maintain a desired range of pressure throughout the network, while the second is focused at finding the optimal regulation of inverters for variable speed pumps in order to minimize energetic costs. An application to a real system is finally presented.

Storfjorden (Svalbard): Modeling of the Polynya Development and the Sea Ice Ridging Process

Remote sensing observations of Storfjorden ice cover described the persistence and evolution of latent heat polynyas during winter 1997/1998. The induced important ice production was quantitatively estimated by simple modeling of the sea ice dynamics and growth. In the present work we used mathematical modeling to qualitatively simulate the polynya open and developing. First, we estimate the values of internal stresses appeared in Storfjorden ice sheet due to the wind stress and used them in the model calibration algorithm. Then, we model the polynya open and developing in simple quasi-static approach. The sea ice ridging process is modeled last and the maximum of ice ridges height is estimated. The results of the simulations are compared to satellite observations from ERS-2. They show that the equilibrium stages of the model developing coincide in common with in-situ data of satellite observations. From another side, the estimations show that the ice ridge keel can achieve height up to 8 m along the eastern shore of Spitsbergen.

Model Calibration for the High-Purity Oxygen Activated Sludge Process – Algorithm Development and Evaluation

A model calibration algorithm is developed for the high-purity oxygen activated sludge process (HPO-ASP). The algorithm is evaluated under different conditions to determine the effect of the following factors on the performance of the algorithm: data quality, number of observations, and number of parameters to be estimated. The process model used in this investigation is the first HPO-ASP model based upon the IAWQ (formerly IAWPRC) Activated Sludge Model No. 1. The objective function is formulated as a relative least-squares function and the non-linear, constrained minimization problem is solved by the Complex method. The stoichiometric and kinetic coefficients of the IAWQ activated sludge model are the parameters focused on in this investigation. Observations used are generated numerically but are made close to the observations from a full-scale high-purity oxygen treatment plant. The calibration algorithm is capable of correctly estimating model parameters even if the observations are severely noise-corrupted. The accuracy of estimation deteriorates gradually with the increase of observation errors. The accuracy of calibration improves when the number of observations (n) increases, but the improvement becomes insignificant when n>96. It is also found that there exists an optimal number of parameters that can be rigorously estimated from a given set of information/data. A sensitivity analysis is conducted to determine what parameters to estimate and to evaluate the potential benefits resulted from collecting additional measurements.