Global Parameter Estimation Research Articles

Development of a methodology for prediction and calibration of parameters of DEM simulations based on machine learning

This research work aims to develop a robust methodology for the global estimation of interaction parameters based on machine learning, applicable to the discrete element method (DEM) in the study of granular materials. The specific objectives include establishing a theoretical framework that relates the interaction micro-parameters with the macro-parameters and the physical behaviour of the material; performing DEM simulations for different material parameters; developing a machine learning-based model for global parameter estimation; and consolidating the methodology for obtaining micro-parameters for a given material and behaviour. The methodology will be applied specifically to the case of dry copper ore, evaluating its limitations and the possibility of extension to materials with other characteristics. This approach does not consider direct experimental tests, but focuses on the characterisation of the relationship between the input parameters of the material and its response through simulations, validating the response and sensitivity of the model in its different stages. The methodology is expected to allow the systematic estimation of interaction properties for a DEM model, considering micro-parameter duplicities and their global selection, aspects little addressed in the literature. The final verification includes mechanisms and key questions that facilitate future modifications and improvements, allowing its application to materials of different characteristics beyond the specific case study.

Determination of global geodetic parameters using satellite laser ranging to Galileo, GLONASS, and BeiDou satellites

The new Global Navigation Satellite System (GNSS) satellites, including GLONASS, Galileo, and BeiDou system, are equipped with Laser Retroreflector Arrays (LRA) to support Satellite Laser Ranging (SLR) tracking, which contributes to the estimation of global geodetic parameters. In this study, we estimate the global geodetic parameters using the SLR observations to GNSS satellites and also investigate the effects of different data processing strategies on the estimated Earth Rotation Parameters (ERP), geocenter motion, and terrestrial scale. The results indicate that setting range bias parameters for each satellite-station pair can effectively account for the satellite-specific biases induced by LRAs, leading to smaller Root Mean Square Errors (RMSE) of the post-fit SLR residuals. Furthermore, estimating the range biases for each satellite-station pair improves the accuracy of the estimated station coordinates and ERP. We also examine the impact of different arc lengths on the estimates of ERP, geocenter motion, and terrestrial scale. The results show that extending arc length can significantly reduce the formal error of ERP. The 7-day strategy produces the smallest RMSEs of 473 microarcseconds and 495 microarcseconds for the estimated X- and Y-component of pole coordinates, and 52 microseconds for length-of-day, respectively. However, the estimated geocenter motion is less affected by the arc length, even the shortest 1-day arc strategy can capture the seasonal variations of geocenter motion in Z component. For scale estimation, extending the arc length notably improves the accuracy of the estimated station coordinates and scale, but this advantage becomes less noticeable in longer arcs. The 7-day solution also obtains the closet scale results compared to ITRF2014, with the RMSE of 2.10 × 10–9.

Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor.

Strategies for Forest Height Estimation by High-Precision DEM Combined with Short-Wavelength PolInSAR TanDEM-X

The purpose of this article is to explore forest height estimation strategies using topographic data (DEM) combined with TanDEM-X while comparing the effect of volume scattering complex coherence selection on forest height estimation in the traditional random volume over ground (RVoG) three-stage algorithm. In this study, four experimental strategies were designed for comparison based on TanDEM-X polarized interferometric synthetic aperture radar (PolInSAR) data, TanDEM-DEM, and 42 field-measured data. Our results show that in the RVoG model, (1) a reference ground phase to select the volume scattering complex coherence provides greater accuracy in determining forest height, (2) forest height estimation can be achieved by directly using DEM as ground phase information without relying on model solving and obtaining a more accurate forest height than TanDEM-X alone, and (3) the highest estimation accuracy is obtained by using DEM as coherence information among all schemes. Although the difference in forest height estimation results is not significant in this study, it still proves that the forest height estimation strategy of high-precision DEM combined with short-wavelength PolInSAR can not only improve the forest height estimation accuracy but also simplify the solving process of the RVoG model, which is an important reference for global forest parameter estimation and ecosystem detection based on spaceborne PolInSAR.

Global hydrological parameter estimates to local applications: Influence of forcing and catchment properties

AbstractData scarcity in many areas around the world represents a major problem for hydrological model calibrations. Global parameter estimates and global forcing can provide possibilities to access hydrological responses in ungauged regions. In this study, we applied HBV global parameter estimates considering uncertainty in the Upper Neckar and Upper Danube catchments, Germany, to answer what are the influencing factors and how good are their local applications. We tested simulations with precipitation in spatial resolutions from 0.05 to 0.2° and with local/global sources. Results show that the general performance is acceptable to good (Kling-Gupta efficiency, KGE: 0.51–0.79) in both catchments using local or global precipitation. The influence of spatial resolutions is insignificant while using local precipitation slightly increases performance in both catchments. Catchment properties such as complex topography and special karst subsurface may lead to a deterioration of performance by 0.2 of median KGE in the Upper Danube compared with the Upper Neckar catchment. The median correlation coefficient, runoff ratio and relative error suggest that using global parameter estimates can reproduce seasonality and long-term water balance in our studied region. Our study highlights the potential of using global parameter estimates and global forcing in ungauged areas.

MLAGO: machine learning-aided global optimization for Michaelis constant estimation of kinetic modeling

BackgroundKinetic modeling is a powerful tool for understanding the dynamic behavior of biochemical systems. For kinetic modeling, determination of a number of kinetic parameters, such as the Michaelis constant (Km), is necessary, and global optimization algorithms have long been used for parameter estimation. However, the conventional global optimization approach has three problems: (i) It is computationally demanding. (ii) It often yields unrealistic parameter values because it simply seeks a better model fitting to experimentally observed behaviors. (iii) It has difficulty in identifying a unique solution because multiple parameter sets can allow a kinetic model to fit experimental data equally well (the non-identifiability problem).ResultsTo solve these problems, we propose the Machine Learning-Aided Global Optimization (MLAGO) method for Km estimation of kinetic modeling. First, we use a machine learning-based Km predictor based only on three factors: EC number, KEGG Compound ID, and Organism ID, then conduct a constrained global optimization-based parameter estimation by using the machine learning-predicted Km values as the reference values. The machine learning model achieved relatively good prediction scores: RMSE = 0.795 and R2 = 0.536, making the subsequent global optimization easy and practical. The MLAGO approach reduced the error between simulation and experimental data while keeping Km values close to the machine learning-predicted values. As a result, the MLAGO approach successfully estimated Km values with less computational cost than the conventional method. Moreover, the MLAGO approach uniquely estimated Km values, which were close to the measured values.ConclusionsMLAGO overcomes the major problems in parameter estimation, accelerates kinetic modeling, and thus ultimately leads to better understanding of complex cellular systems. The web application for our machine learning-based Km predictor is accessible at https://sites.google.com/view/kazuhiro-maeda/software-tools-web-apps, which helps modelers perform MLAGO on their own parameter estimation tasks.

Correlation Analysis between Urban Green Space and Land Surface Temperature from the Perspective of Spatial Heterogeneity: A Case Study within the Sixth Ring Road of Beijing

Urban greening has been widely regarded as the most effective, lasting, and economical strategy for alleviating the effects of urban heat islands (UHIs). Previous studies on the cooling effect of urban green spaces (UGSs) tend to analyze the correlation between landscape metrics and land-surface temperature (LST) based on a global parameter estimation, while ignoring urban heterogeneity and autocorrelation. This study focuses on the sixth ring road of Beijing and uses Landsat 8 imagery to retrieve the LST and extract the position of UGSs. We propose a new approach to optimize the selection of landscape metrics, to identify the least and most effective metrics to establish a geographically weighted regression (GWR) model, and to plot the distribution of local regression coefficients to investigate the spatially heterogeneous cooling effects of greenspaces. The effect of UGS landscape metrics on the LST differs according to spatial location; the method enhances our understanding of the effects of UGS spatial configuration on UHIs and better guides the planning and construction of future UGSs.

Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?

Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.

Modified Lévy flight distribution algorithm for global optimization and parameters estimation of modified three-diode photovoltaic model

Many real-world problems demand optimization, minimization of costs and maximization of profits, and meta-heuristic algorithms have proficiently proved their ability to achieve optimum results. This study proposes an alternative algorithm of Lévy Flight Distribution (LFD) by integrating Opposition-based learning (OBL) operator, termed LFD-OBL, for resolving intrinsic drawbacks of the canonical LFD. The proposed approach adopts OBL operator for catering search stagnancy to ensure faster convergence rate. We validate the usefulness of our approach through IEEE CEC’20 test suite, and compare results with original LFD and several other counterparts such as Moth-flame optimization, whale optimization algorithm, grasshopper optimisation algorithm, thermal exchange optimization, sine-cosine algorithm, artificial ecosystem-based optimization, Henry gas solubility optimization, and Harris’ hawks optimization. To further validate the efficiency of LFD-OBL, we apply it on parameters optimization of Solar Cell based on the Three-Diode Photovoltaic model. The qualitative and quantitative results of all the experiments performed in this study suggest superiority of the proposed method.

Toward Quality of Information Aware Distributed Machine Learning

In the era of big data, data are usually distributed across numerous connected computing and storage units (i.e., nodes or workers). Under such an environment, many machine learning problems can be reformulated as a consensus optimization problem, which consists of one objective and constraint terms splitting into N parts (each corresponds to a node). Such a problem can be solved efficiently in a distributed manner via Alternating Direction Method of Multipliers ( ADMM ). However, existing consensus optimization frameworks assume that every node has the same quality of information (QoI) , i.e., the data from all the nodes are equally informative for the estimation of global model parameters. As a consequence, they may lead to inaccurate estimates in the presence of nodes with low QoI. To overcome this challenge, in this article, we propose a novel consensus optimization framework for distributed machine-learning that incorporates the crucial metric, QoI. Theoretically, we prove that the convergence rate of the proposed framework is linear to the number of iterations, but has a tighter upper bound compared with ADMM . Experimentally, we show that the proposed framework is more efficient and effective than existing ADMM -based solutions on both synthetic and real-world datasets due to its faster convergence rate and higher accuracy.

State, global, and local parameter estimation using local ensemble Kalman filters: Applications to online machine learning of chaotic dynamics

AbstractIn a recent methodological article, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we investigate more systematically the possibility of using a local ensemble Kalman filter with either covariance localisation or local domains, in order to retrieve the state and a mix of key global and local parameters. Global parameters are meant to represent the surrogate dynamical core, for instance through a neural network, which is reminiscent of data‐driven machine learning of dynamics, while the local parameters typically stand for the forcings of the model. Aiming at joint state and parameter estimation, a family of algorithms for covariance and local domain localisation is proposed. In particular, we show how to update global parameters rigorously using a local‐domain ensemble Kalman filter (EnKF) such as the local ensemble transform Kalman filter (LETKF), an inherently local method. The approach is tested with success on the 40‐variable Lorenz model using several of the local EnKF flavors. A two‐dimensional illustration based on a multilayer Lorenz model is finally provided. It uses radiance‐like nonlocal observations. It features both local domains and covariance localisation, in order to learn the chaotic dynamics and the local forcings. This article addresses more generally the key question of online estimation of both global and local model parameters.

Modelling of the photo-Fenton process with flexible hydrogen peroxide dosage: Sensitivity analysis and experimental validation

The supply of hydrogen peroxide (H2O2) controlling the amount of highly oxidant hydroxyl radicals is the most critical operational issue for the photo-Fenton process. Accordingly, this study addresses the development of a model for photo-Fenton processes including a flexible H2O2 supply given as a function of time. The model is aimed at its future exploitation in treatment optimization and the determination of the optimal profile for H2O2 supply. The work has adopted a photo Fenton model previously reported that includes the inlet flow (fed-batch) and describes the system dynamics under a flexible dosage. Thus, model global sensitivity analysis (GSA) and parameter estimation were performed using Simulink® to examine the behavior of the model under flexible H2O2 dosage. GSA was carried out using partial rank correlation methods and the Latin hypercube sampling to assess to which extent variations of the model parameters affect each measured response (H2O2, total organic carbon, TOC, and dissolved oxygen, O2 –the experimentally available information). Hence, the model is discussed in regard of its hypothesis and chances for reducing its complexity. This resulted in the rejection of two reactions of the initial model. Next, a set of 12 kinetic, stoichiometric and operative parameters was estimated through the fitting of H2O2, TOC, and O2 profiles. Discussion on model fitting includes computational issues, the role of initial values for the estimation process, the goodness of fit criteria, and the sampling method. The model was fit to experimental data with assorted H2O2 supply profiles and validated, and Root Mean Square Error (RMSE) below 0.009 mM, 0.42 mM, and 0.127 mM were obtained for TOC, H2O2 and O2, respectively. Therefore, this work contributes a practical model aimed at providing model-based optimization for the H2O2 dosage profile of the photo-Fenton process.

Data-Based and Opportunistic Integral Concurrent Learning for Adaptive Trajectory Tracking During Switched FES-Induced Biceps Curls.

Hybrid exoskeletons, which combine functional electrical stimulation (FES) with a motorized testbed, can potentially improve the rehabilitation of people with movement disorders. However, hybrid exoskeletons have inherently nonlinear and uncertain dynamics, including combinations of discrete modes that switch between different continuous dynamic subsystems, which complicate closed-loop control. A particular complication is the uncertain muscle control effectiveness associated with FES. In this work, adaptive integral concurrent learning (ICL) motor and FES controllers are developed for a hybrid biceps curl exoskeleton, which are designed to achieve opportunistic and data-based learning of the uncertain human and electromechanical testbed parameters. Global exponential trajectory tracking and parameter estimation errors are proven through a Lyapunov-based stability analysis. The motor effectiveness is assumed to be unknown, and, to help with fatigue reduction, FES is enabled to switch between multiple electrodes on the biceps brachii, further complicating the analysis. A consequence of switching between the different uncertain subsystems is that the parameters must be opportunistically learned for each subsystem (i.e. each electrode and the motor), while that subsystem is active. Experiments were performed to validate the developed ICL controllers on twelve healthy participants. The average (± standard deviation) position tracking errors across each participant were 1.44 ± 5.32 deg, -0.25 ± 2.85 deg, and -0.17 ± 2.66 deg across biceps Curls 1-3, 4-7, and 8-10, respectively, where the average across the entire experiment was 0.28 ± 3.53 deg.

Global Nonlinear Aerodynamic Reduced-Order Modeling and Parameter Estimation by Radial Basis Functions

AbstractThis work presents a novel global reduced-order modeling and parameter estimation of a maneuvering aircraft up to poststall angles of attack using radial basis functions. A computational fl...

Fitting thermodynamic-based models: Incorporating parameter sensitivity improves the performance of an evolutionary algorithm

A detailed comprehension of transcriptional regulation is critical to understanding the genetic control of development and disease across many different organisms. To more fully investigate the complex molecular interactions controlling the precise expression of genes, many groups have constructed mathematical models to complement their experimental approaches. A critical step in such studies is choosing the most appropriate parameter estimation algorithm to enable detailed analysis of the parameters that contribute to the models.In this study, we develop a novel set of evolutionary algorithms that use a pseudo-random Sobol Set to construct the initial population and incorporate parameter sensitivities into the adaptation of mutation rates, using local, global, and hybrid strategies. Comparison of the performance of these new algorithms to a number of current state-of-the-art global parameter estimation algorithms on a range of continuous test functions, as well as synthetic biological data representing models of gene regulatory systems, reveals improved performance of the new algorithms in terms of runtime, error and reproducibility. In addition, by analyzing the ability of these algorithms to fit datasets of varying quality, we provide the experimentalist with a guide to how the algorithms perform across a range of noisy data.These results demonstrate the improved performance of the new set of parameter estimation algorithms and facilitate meaningful integration of model parameters and predictions in our understanding of the molecular mechanisms of gene regulation.

Analysis on the Difference in the Initial Examination Results of Postgraduates Based on Regression Discontinuity Design

The high grades in postgraduates entrance examination are the stepping stone to improve the professional competition in China, which makes the critical influence factors to the initial examination of postgraduates as a hot topic. In order to measure the correlation between the academic performance of undergraduate students and the probability of successful postgraduate entrance examination, and find some effective ways to improve the success rate in the postgraduate entrance examination, we design regression discontinuity model to search the causal correlation between the preliminary entrance exam and CET-6 scores of candidates. Global parameter estimation and local non-parameter estimation were estimated respectively to improve the accuracy of model fitting. In addition, the validity and robustness of the experiment were tested by sensitivity analysis. The results show that the students who get better grades in college are more likely to have a positive effect in the preliminary entrance examination, and make the success rate of postgraduate entrance examination higher.

Global Approach for Simulated Moving Bed Model Identification: Design of Experiments, Uncertainty Evaluation, and Optimization Strategy Assessment

Simulated moving bed (SMB) chromatography is a widely used technique for the resolution of compounds difficult to separate. SMB parameter estimation is traditionally carried out following a time and money consuming series of experiments in an SMB unit where deviations may arise. This work aims to present a novel global and straightforward parameter estimation procedure together with uncertainty analysis. Particle swarm optimization (PSO) is employed to search for parameters in an eight-dimensional space, avoid local minima, and enable uncertainty analysis. The proposed methodology is validated in a software-in-the-loop approach. A new parameter estimation is then carried out using the data of one experimental run from the literature, together with uncertainty evaluation based on the PSO-generated population that enables model validation and definition of confidence regions for the model. A robust method for the parameter estimation of an SMB unit is presented in order to produce a more precise and reliable model. In addition, it also significantly reduces the number of necessary steps for parameter estimation, leading to a more efficient procedure. The results show that it is possible to perform parameter estimation from SMB chromatography producing a more trustworthy model.

Pengujian Hipotesis Parameter Model Mixed Geographically Weighted Regression Data Indeks Pembangunan Manusia di Kalimantan Tahun 2016

Mixed Geographically Weighted Regression (MGWR) model is a Geographically Weighted Regression (GWR) model with some parameters are global (have the same value) and several other parameters are local (have different values) for each observation location. The purpose of this study is to obtain a MGWR model on the Human Development Index (HDI) data and find out the factors that influence the HDI of each district (city) in the provinces of East Kalimantan, Central Kalimantan and South Kalimantan in 2016. The parameter estimation method is carried out through two stages (backshift), namely local parameter estimation by using the Weighted Least Square (WLS) method and global parameter estimation by using the Ordinary Least Square (OLS) method. Spatial weighting on local parameter estimation is obtained by using an adaptive Bisquare weighting functions, where optimum bandwidth determination uses Generalized Cross-Validation (GCV) criterion. Based on the result of MGWR parameter testing, it was concluded that the school enrollment rates (SMP) affected the HDI of all districts (cities) in East Kalimantan, Central Kalimantan and South Kalimantan, while the population density affects the HDI only in a few districts (cities), namely East Kutai, Balikpapan, Samarinda and Bontang.

Penerapan Model Mixed Geographically Weighted Regression dengan Fungsi Pembobot Adaptive Tricube pada IPM 30 Kabupaten/Kota di Provinsi Kalimantan Timur, Kalimantan Tengah dan Kalimantan Selatan Tahun 2016

Mixed Geographically Weighted Regression (MGWR) model is a Geographically Weighted Regression (GWR) model which has global (equal value) and local (inequal value) parameters at every different observation location. The goal of this study is to obtain MGWR model of the Human Development Index (HDI) data and find out significant factors influencing the HDI in each district (city) East Kalimantan, Central Kalimantan and South Kalimantan province in 2016. Parameter estimation method is conducted in two stages namely local parameter estimation and global parameter estimation. Local parameter estimation method is Maximum Likelihood Estimation (MLE), with spatial weighting is calculated by adaptive tricube weighting function and optimum bandwidth determination uses the Akaike Information Criteria (AIC). Global parameter estimation method is Ordinary Least Square (OLS). Based on the result of MGWR parameter testing, it was concluded that the school enrollment rates (SMP) and poor people percentage affected the HDI of 30 districts (cities) in East Kalimantan, Central Kalimantan and South Kalimantan. Meanwhile the population density affected the HDI of two districts namely HDI of Samarinda and Bontang.

Underwater degraded image–sharpening method based on optimal polarization parameter reconstruction

In order to solve the problems of blurred image and low contrast caused by the absorption and scattering of underwater light by turbid water, an algorithm of underwater image optimal restoration based on global polarization parameter estimation was proposed. Firstly, the local minimum filter was used to estimate the underwater background light image, Stokes vector principle was introduced to calculate the degree of polarization image, and normalized mutual information was used to further optimize the degree of polarization information, to obtain the best reconstructed polarization parameters in the imaging region. Secondly, a method of image reconstruction based on morphology was used to estimate the infinite underwater background light intensity values automatically. Finally, the underwater simulated environment platform was built, and the underwater polarization image was acquired in real time through a single channel fast rotating polarization detector. In order to verify the effectiveness of the algorithm, the three objective evaluation indexes were adopted as quantification to evaluate indexes factors. The results show that the algorithm is better than the other underwater image restoration methods.