Efficient Parameter Estimation Research Articles

SBMLToolkit.jl: a Julia package for importing SBML into the SciML ecosystem.

Julia is a general purpose programming language that was designed for simplifying and accelerating numerical analysis and computational science. In particular the Scientific Machine Learning (SciML) ecosystem of Julia packages includes frameworks for high-performance symbolic-numeric computations. It allows users to automatically enhance high-level descriptions of their models with symbolic preprocessing and automatic sparsification and parallelization of computations. This enables performant solution of differential equations, efficient parameter estimation and methodologies for automated model discovery with neural differential equations and sparse identification of nonlinear dynamics. To give the systems biology community easy access to SciML, we developed SBMLToolkit.jl. SBMLToolkit.jl imports dynamic SBML models into the SciML ecosystem to accelerate model simulation and fitting of kinetic parameters. By providing computational systems biologists with easy access to the open-source Julia ecosystevnm, we hope to catalyze the development of further Julia tools in this domain and the growth of the Julia bioscience community. SBMLToolkit.jl is freely available under the MIT license. The source code is available at https://github.com/SciML/SBMLToolkit.jl.

Likelihood function derivatives for a linear mixed model with compound symmetry assumption

The paper explores the properties of linear mixed models with simple random effects of the form: yi = Xiβ + ZiYi + εi, i = 1, . . . ,M, Yi ∼ N(0, Ψ), εi ∼ Т(0, σ2I), where M is the number of distinct groups, each consisting of ni observations. Random effects Yi and within-group errors εi are independent across different groups and within the same group. β is a p-dimensional vector of fixed effects, Yi is a q-dimensional vector of random effects, and Xi and Zi are known design matrices of dimensions nixp and nixq, of fixed and random effects respectively. Vectors εi represent within-group errors with a spherically Gaussian distribution.Assuming a compound symmetry in the correlation structure of the matrix Ψ governing the dependence among within-group errors, analytical formulas for the first two partial derivatives of the profile restricted maximum likelihood function with respect to the correlation parameters of the model are derived. The analytical representation of derivatives facilitates the effective utilization of numerical algorithms like Newton-Raphson or Levenberg-Marquardt.The restricted maximum likelihood (REML) estimation is a statistical technique employed to estimate the parameters within a mixed-effects model, particularly in the realm of linear mixed models. It serves as an extension of the maximum likelihood estimation method, aiming to furnish unbiased and efficient parameter estimates, especially in scenarios involving correlated data. Within the framework of the REML approach, the likelihood function undergoes adjustments to remove the nuisance parameters linked to fixed effects. This modification contributes to enhancing the efficiency of parameter estimation, particularly in situations where the primary focus is on estimating variance components or when the model encompasses both fixed and random effects.

Online state and time‐varying parameter estimation using the implicit equal‐weights particle filter

AbstractA method is proposed for resilient and efficient estimation of the states and time‐varying parameters in nonlinear high‐dimensional systems through a sequential data assimilation process. The importance of estimating time‐varying parameters lies not only in improving prediction accuracy but also in determining when model characteristics change. We propose a particle‐filter‐based method that incorporates nudging techniques inspired by optimization algorithms in machine learning by taking advantage of the flexibility of the proposal density in particle filtering. However, as the model resolution and number of observations increase, filter degeneracy tends to be the obstacle to implementing the particle filter. Therefore, this proposed method is combined with the implicit equal‐weights particle filter (IEWPF), in which all particle weights are equal. The method is validated using the 1000‐dimensional linear model with an additive parameter and the 1000‐dimensional Lorenz‐96 model, where the forcing term is parameterized. The method is shown to be capable of resilient and efficient parameter estimation for parameter changes over time in our application with a linear observation operator. This leads to the conjecture that it applies to realistic geophysical, climate, and other problems.

An efficient data sheet based parameter estimation technique of solar PV

This work develops an efficient parameter estimation technique, based on manufacturer datasheet, to obtain unknown parameter of solar photovoltaic (PV), precisely. Firstly, a nonlinear least square objective function, in terms of variables given in manufacturer datasheet, has been developed. Then, two optimization techniques, namely the Particle Swarn Optimization (PSO) and Harmony Search (HS) are applied on the developed objective function to achieve the optimized result. Further, the correctness of the developed technique is tested by estimating the performance indices, namely percentage maximum power deviation index (%MPDI) and overall model deviation index (OMDI), of two different solar PV, viz., Kyocera KD210GH-2PU (poly-crystalline), and Shell SQ85 (mono-crystalline). It is shown that developed method with PSO outperforms the HS. The developed method with PSO gives the values of %MPDI and OMDI of 0.0214% and 0.213, only. Also, the existing methods, based on hybrid, multi-objective function, numerical method, have been considered for the comparative analysis. It is revealed through the comparative studies that the developed method with PSO has smaller value of MPDI (= 0.0041%) and OMDI (0.005) than the other existing methods. Further, the convergence of the developed method has also been estimated to check the speed of estimation. It is shown that the developed technique converges only in 5 s. In addition, the developed technique avoids the need of extensive data as it is based on manufacturer datasheet.

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

A 2PLM-RANK multidimensional forced-choice model and its fast estimation algorithm.

High-stakes non-cognitive tests frequently employ forced-choice (FC) scales to deter faking. To mitigate the issue of score ipsativity derived, many scoring models have been devised. Among them, the multi-unidimensional pairwise preference (MUPP) framework is a highly flexible and commonly used framework. However, the original MUPP model was developed for unfolding response process and can only handle paired comparisons. The present study proposes the 2PLM-RANK as a generalization of the MUPP model to accommodate dominance RANK format response. In addition, an improved stochastic EM (iStEM) algorithm is devised for more stable and efficient parameter estimation. Simulation results generally supported the efficiency and utility of the new algorithm in estimating the 2PLM-RANK when applied to both triplets and tetrads across various conditions. An empirical illustration with responses to a 24-dimensional personality test further supported the practicality of the proposed model. To further aid in the application of the new model, a user-friendly R package is also provided.

Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis

The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.

Parameter-by-parameter estimation method for adsorption isotherm in hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC) is used as a critical polishing step in the downstream processing of biopharmaceuticals. Normally the process development of HIC is a cumbersome and time-consuming task, and the mechanical models can provide a powerful tool to characterize the process, assist process design and accelerate process development. However, the current estimation of model parameters relies on the inverse method, which lacks an efficient and logical parameter estimation strategy. In this study, a parameter-by-parameter (PbP) method based on the theoretical derivation and simplifying assumptions was proposed to estimate the Mollerup isotherm parameters for HIC. The method involves three key steps: (1) linear regression (LR) to estimate the salt-protein interaction parameter and the equilibrium constant; (2) linear approximation (LA) to estimate the stoichiometric parameter and the maximum binding capacity; and (3) inverse method to estimate the protein-protein interaction parameter and the kinetic coefficient. The results indicated that the LR step should be used for dilution condition (loading factor below 5%), while the LA step should be conducted when the isotherm is in the transition or nonlinear regions. Six numerical experiments were conducted to implement the PbP method. The results demonstrated that the PbP method developed allows for the systematic estimation of HIC parameters one-by-one, effectively reducing the number of parameters required for inverse method estimation from six to two. This helps prevent non-identifiability of structural parameters. The feasibility of the PbP-HIC method was further validated by real-world experiments. Moreover, the PbP method enhances the mechanistic understanding of adsorption behavior of HIC and shows a promising application to other stoichiometric displacement model-derived isotherms.

Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians

Efficient delay and parameter estimation for nonlinear systems based on lifted IRK integrators with inexact Jacobians

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference

A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic (GARCH) process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed multivariate heavy-tailed count time series model via maximum likelihood method is challenging since the likelihood function involves a Bessel function that depends on the multivariate counts and its dimension. As a consequence, numerical instability is often experienced in optimization procedures. To overcome this computational problem, two feasible variants of the expectation-maximization (EM) algorithm are proposed for estimating the parameters of our model under low and high-dimensional settings. These EM algorithm variants provide computational benefits and help avoid the difficult direct optimization of the likelihood function from the proposed process. Our model and proposed estimation procedures can handle multiple features such as modeling of multivariate counts, heavy-tailedness, overdispersion, accommodation of outliers, allowances for both positive and negative autocorrelations, estimation of cross/contemporaneous-correlation, and the efficient estimation of parameters from both statistical and computational points of view. Extensive Monte Carlo simulation studies are presented to assess the performance of the proposed EM algorithms. Two empirical applications of our approach are provided. The first application concerns modeling bivariate count time series data on cannabis possession-related offenses in Australia, while the second one involves modeling intraday high-frequency financial transactions data from multiple holdings in the U.S. financial market.

A Poisson Lognormal-Lindley model for simultaneous estimation of multiple crash-types: Application of multivariate and pooled univariate models

Challenges addressing overdispersion, unobserved heterogeneity, the preponderance of zeros, and correlation in the dependent variables of crash count models are of significant interest. Accounting for all these data issues simultaneously is few and far between. This study proposes a new mixing distribution model that accounts for overdispersion and the preponderance of zeros in crash count models. The proposed mixing distribution model extends to the multivariate structure to account for correlations between dependent variables and unobserved heterogeneity. The empirical analysis is conducted on crash data of Bruce highway involving single-vehicle and multi-vehicle crash types by “fatal and severe injury” and “moderate and minor injury” severity levels on aggregated data over three analysis years (2016, 2017, and 2018). The study demonstrates superior goodness of fit of the proposed multivariate random parameters Poisson lognormal-Lindley model compared to its restricted models. Moreover, pooling the crash data as repeated measures of crash types helped formulate a pooled-univariate random parameters Poisson-Lindley model to estimate multiple crash types by severity. The results showed the pooled-univariate model offers comparable goodness of fit and averaged marginal effects as the complex multivariate modeling structure. Moreover, the proposed pooled-univariate model reduced the model complexity to a one-dimensional integral and offered more efficient parameter estimates. In the empirical context, the modeling results showed that single-vehicle and multi-vehicle crashes by severity are linked with different causality.

Thermo-Electrochemical Simulation of Large-Format Li-Ion Cells in 3D Using the Battery Modelling Toolbox (BattMo)

Computer-based modelling and simulation can be a valuable tool when developing electrochemical devices: it offers possibilities for insight into internal properties not available in experiments, it can guide the development and testing of new materials in the device, it can provide time-efficient alternatives for optimizing operating procedures, and more. In this contribution we will give an overview of the Battery Modelling Toolbox (BattMo), which is an open-source framework for continuum modelling of electrochemical-thermal systems. It has been primarily developed for the modelling and simulation of Li-ion battery cells using pseudo X-dimensional (PXD, X=2,3,4) Doyle-Fuller-Newman models, but has also successfully been applied to electrolyzers. BattMo is developed in MATLAB and has a high-performance Julia version (BattMo.jl) in development.The fundamental equations of mass, charge and energy conservation are in BattMo discretized using a low-order implicit finite volume method. These are suitable methods, since they are conservative (meaning that mass, charge, etc., are conserved), and guarantee monotone solutions (meaning that the solutions will be positive if the data is positive). These properties provide a simulation foundation that is robust and stable also on complex 3D grids -- essential features when modelling real-world systems. As with most numerical methods, the most time-consuming part is to solve the resulting linear system of equations. In BattMo we make use of state-of-the-art block-wise multigrid methods to obtain high performance.Working with BattMo may be done using a GUI, which generates a json file which completely specifies a simulation. This json file can be used directly as input to BattMo via the MATLAB/Julia prompt, or used in cloud resources. It is also possible to use a json file as a base configuration and modify the parameters manually or programmatically, for example to investigate a specific system response when changing some parameters of interest. BattMo also provides functionality for automatic gradient-based optimization and parameter estimation that can be used for maximizing or minimizing some goal quantity, and matching to experimental data. A key component for performing efficient gradient-based optimization and parameter estimation in the case of many parameters (for example when having one parameter value in each grid cell) is the use of so-called adjoints. Using adjoints allow for the gradients in the sensitivity analysis to be computed with a constant cost that is independent on the number of parameters, thus avoiding the curse of dimensionality.Much attention is spent on making the BattMo json input compatible with other simulation frameworks such as PyBamm, COMSOL and CideMod. This is to accelerate research and development by taking advantage of the strengths of different packages, as well as providing not only reproducible but also reliable science. BattMo is developed alongside BattINFO, which is a battery interface ontology based on EMMO (Elementary Multiperspective Material Ontology) that is developed in the BIG-MAP EU H2020 project. We also seek to support the BPX standard developed by the PyBamm team.In this talk we will overview the basic features of BattMo and see how the modular approach used in the software simplifies development of new models. BattMo contains many examples, and we will here present thermal simulation of 1D and 3D cells with LFP and LNMO battery chemistries in pouch cell format and investigate the effects of the tabless design in the 4680 cylindrical cell format (see the Figure below).BattMo is available at https://github.com/BattMoTeam and is developed with the support from the EU H2020 innovation programs under the grants Hydra (875527) and BIG-MAP (957189). Figure 1

Efficient estimation of pharmacokinetic parameters from breast dynamic contrast-enhanced MRI based on a convolutional neural network for predicting molecular subtypes

Objective. Tracer kinetic models allow for estimating pharmacokinetic (PK) parameters, which are related to pathological characteristics, from breast dynamic contrast-enhanced magnetic resonance imaging. However, existing tracer kinetic models subject to inaccuracy are time-consuming for PK parameters estimation. This study aimed to accurately and efficiently estimate PK parameters for predicting molecular subtypes based on convolutional neural network (CNN). Approach. A CNN integrating global and local features (GL-CNN) was trained using synthetic data where known PK parameters map was used as the ground truth, and subsequently used to directly estimate PK parameters (volume transfer constant K trans and flux rate constant K ep) map. The accuracy assessed by the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and concordance correlation coefficient (CCC) was compared between the GL-CNN and Tofts-based PK parameters in synthetic data. Radiomic features were calculated from the PK parameters map in 208 breast tumors. A random forest classifier was constructed to predict molecular subtypes using a discovery cohort (n = 144). The diagnostic performance evaluated on a validation cohort (n = 64) using the area under the receiver operating characteristic curve (AUC) was compared between the GL-CNN and Tofts-based PK parameters. Main results. The average PSNR (48.8884), SSIM (0.9995), and CCC (0.9995) between the GL-CNN-based K trans map and ground truth were significantly higher than those between the Tofts-based K trans map and ground truth. The GL-CNN-based K trans obtained significantly better diagnostic performance (AUCs = 0.7658 and 0.8528) than the Tofts-based K trans for luminal B and HER2 tumors. The GL-CNN method accelerated the computation by speed approximately 79 times compared to the Tofts method for the whole breast of all patients. Significance. Our results indicate that the GL-CNN method can be used to accurately and efficiently estimate PK parameters for predicting molecular subtypes.

Validating Posteriors Obtained by an Emulator When Jointly Fitting Mock Data of the Global 21 cm Signal and High-z Galaxy UV Luminosity Function

Although neural-network-based emulators enable efficient parameter estimation in 21 cm cosmology, the accuracy of such constraints is poorly understood. We employ nested sampling to fit mock data of the global 21 cm signal and high-z galaxy ultraviolet luminosity function (UVLF) and compare for the first time the emulated posteriors obtained using the global signal emulator globalemu to the “true” posteriors obtained using the full model on which the emulator is trained using ARES. Of the eight model parameters we employ, four control the star formation efficiency (SFE) and thus can be constrained by UVLF data, while the remaining four control UV and X-ray photon production and the minimum virial temperature of star-forming halos () and thus are uniquely probed by reionization and 21 cm measurements. For noise levels of 50 and 250 mK in the 21 cm data being jointly fit, the emulated and “true” posteriors are consistent to within 1σ. However, at lower noise levels of 10 and 25 mK, globalemu overpredicts and underpredicts γ lo, an SFE parameter, by ≈3σ–4σ, while the “true” ARES posteriors capture their fiducial values within 1σ. We find that jointly fitting the mock UVLF and 21 cm data significantly improves constraints on the SFE parameters by breaking degeneracies in the ARES parameter space. Our results demonstrate the astrophysical constraints that can be expected for global 21 cm experiments for a range of noise levels from pessimistic to optimistic, as well as the potential for probing redshift evolution of SFE parameters by including UVLF data.

Curriculum-based humanoid robot identification using large-scale human motion database

Identifying an accurate dynamics model remains challenging for humanoid robots. The difficulty is mainly due to the following two points. First, a good initial model is required to evaluate the feasibility of motions for data acquisition. Second, a highly nonlinear optimization problem needs to be solved to design movements to acquire the identification data. To cope with the first point, in this paper, we propose a curriculum of identification to gradually learn an accurate dynamics model from an unreliable initial model. For the second point, we propose using a large-scale human motion database to efficiently design the humanoid movements for the parameter identification. The contribution of our study is developing a humanoid identification method that does not require the good initial model and does not need to solve the highly nonlinear optimization problem. We showed that our curriculum-based approach was able to more efficiently identify humanoid model parameters than a method that just randomly picked reference motions for identification. We evaluated our proposed method in a simulation experiment and demonstrated that our curriculum was led to obtain a wide variety of motion data for efficient parameter estimation. Consequently, our approach successfully identified an accurate model of an 18-DoF, simulated upper-body humanoid robot.

A Generalized Class of Log-Type Estimators of Finite Population Mean Based on Correlation Coefficient

In sampling theory, it is a popular trend to use auxiliary information to obtain more efficient estimators for the population parameters to increase the precision of the estimator. Estimators obtained using auxiliary information are supposed to be more efficient than the estimators obtained without using auxiliary information. The ratio, regression, product and difference methods take advantage of the auxiliary information at the estimation stage. Therefore, this study considered a generalized class of log-type estimators of finite population mean based on correlation coefficient as the proposed estimator for estimating the population mean of the study variable. It has been shown that the generalized class of log-type estimators has lesser mean square errors (MSEs) under the optimum values of the characterizing scalar as compared to some of the commonly used related estimators available in the literature. Further, an extension of the proposed generalized class of log-type estimators using multiple auxiliary variables such as coefficient of variation, coefficient of kurtosis , and correlation coefficient. have also base initiated in this dissertation. The expressions for the properties of the proposed family of estimators, that is; Bias and Mean Square Error (MSE), were derived to the first degree of approximation. We also obtained the optimum Mean Square Error (MSEopt.), and theoretical comparisons were made with the related existing estimators in literature. Following theoretical comparisons, it was demonstrated that the proposed family of estimators was more efficient than various related existing estimators compared with, under the obtained conditions.

Personalised parameter estimation of the cardiovascular system: Leveraging data assimilation and sensitivity analysis

Detailed models of dynamical systems used in the life sciences may include hundreds of state variables and many input parameters, often with physical meanings. Therefore, efficient and unique input parameter identification, from experimental data, is an essential but challenging task for this class of models. This study presents a comprehensive analysis of a nine-dimensional single ventricle lumped-parameter model, representing the systemic circulation. This model is formulated in terms of differential algebraic equations, often found in other areas of the life sciences. We introduce a novel computational algorithm designed to incorporate patient-specific beat-to-beat variability into model investigations, utilising the Unscented Kalman Filter (UKF) for efficient parameter estimation. Our findings demonstrate the exceptional adaptability of the UKF to severe parameter perturbations, representing significant physiological changes. Furthermore, we provide novel insights into the continuous sensitivity of model input parameters, illustrating the robustness and efficacy of UKF. The monitoring of a patient’s physiological state, with minimal delay, becomes feasible, by incorporating patient-specific measurements and leveraging the UKF. The workflow presented in this paper enables prompt identification of pathophysiological conditions and will improve patient care.

Hybrid generative model for grading the severity of diabetic retinopathy images

ABSTRACT One of the common eye conditions affecting patients with diabetes is diabetic retinopathy (DR). It is characterised by the progressive impairment to the blood vessels with the increase of glucose level in the blood. The grading efficiency still finds challenging because of the existence of intra-class variations and imbalanced data distributions on the retinal images. Traditional machine learning techniques utilise hand-engineered features for classification of the affected retinal images. As convolutional neural network produces better image classification accuracy in many medical images, this work utilises the CNN-based feature extraction method. This feature has been used to build Gaussian mixture model (GMM) for each class that maps the CNN features to log-likelihood dimensional vector spaces. Since the Gaussian mixture model can be realised as a mixture of both parametric and nonparametric density models and has their flexibility in capturing different data distributions, probabilistic outputs, interpretability, efficient parameter estimation, and robustness to outliers, the proposed model aimed to obtain and provide a smooth approximation of the underlying distribution of features for training the model. Then these vector spaces are trained by the SVM classifier. Experimental results illustrate the efficacy of the proposed model with accuracy 86.3% and 89.1%, respectively.

Factors of Using Long Acting and Permanent Methods (LAPM) of Contraception: Bangladesh Perspective

The Government of Bangladesh is very much aware of controlling excessive birth rate to maintain population problem. Though Bangladesh is owning self-sufficiency in many sectors, the increasing population is a great impediment for the development of the country. So, promoting different contraceptive methods is of much importance. This work aims at identifying the important determinants that affect the long-acting and permanent methods (LAPM) of contraception. Firstly, chi-square test of association is carried out for defining the correlates of LAPM of contraception using Bangladesh Demographic and Health Survey (BDHS), 2017-18 data. For estimating the effects of each controlled independent variables, data are further analyzed within a multivariate framework. To obtain consistent and efficient estimates of parameters of interest, multinomial logistic regression model is used in this work. The study finds several socio-economic and demographic variables having high impact on using LAPM. The study findings are properly discussed and recommendations are made accordingly for the policy makers.
 Dhaka Univ. J. Sci. 71(2): 87-94, 2023 (July)

Semi-Physical Modeling of Soft Pneumatic Actuators With Stiffness Tuning

Abstract The inherent low stiffness in soft robots makes them preferable for working in close proximity to humans. However, having this low stiffness creates challenges when operating in terms of control and sensitivity to disturbances. To alleviate this issue, soft robots often have built-in stiffness tuning mechanisms that allow for controlled increases in stiffness. Additionally, redundant pneumatic manipulators can utilize antagonistic pressure to achieve identical positions under increased stiffness. In this paper, we develop a model to predict the stiffness and configuration of a pneumatic soft manipulator under different pressure inputs and external forces. The model is developed based on the physical characteristics of a soft manipulator while enabling efficient parameter estimation and computation. The efficacy of the modeling approach is supported via experimental results.