Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology

2018 ◽  
Vol 26 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Valeriya V. Zheltkova ◽  
Dmitry A. Zheltkov ◽  
Zvi Grossman ◽  
Gennady A. Bocharov ◽  
Eugene E. Tyrtyshnikov
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Optimization Techniques ◽  
Computational Method ◽  
Parameter Estimation Problem ◽  
Multiscale Models ◽  
Computational Tools ◽  
Systems Immunology ◽  
Estimation Problems ◽  
Standard Parameter

AbstractThe development of efficient computational tools for data assimilation and analysis using multi-parameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model. The data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.

scholarly journals Modelling HIV infection: model identification and global sensitivity analysis

2019 ◽  
Vol 14 (1) ◽  
pp. 19-33 ◽  
Author(s):  
V.V Zheltkova ◽  
D.A. Zheltkov ◽  
G.A. Bocharov
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Hiv Infection ◽  
Global Sensitivity Analysis ◽  
Immune Cell ◽  
Estimation Problem ◽  
Infection Model ◽  
Parameter Estimation Problem ◽  
Global Sensitivity ◽  
Systems Immunology

Mathematical modelling can be very useful in studying complex objects in modern systems immunology. In this work we studied the problem of modelling immune cell population dynamics for HIV infection through the set of models with different levels of complexity, which include several characteristics of HIV infection dynamics (antigen presenting, cell and humoral immune reactions, the effect of regulatory T-lymphocytes). We formulated and solved the parameter estimation problem using maximal likelihood approach, for two variants of modelling error quantifying. The global sensitivity analysis was implemented with LHS-PRCC method. Models were compared by the residual functional values and using the information-theoretical framework. We present the extended Marchuk-Petrov model for HIV infection with delays. For solving the parameter estimation problem for this model we compared a number of numerical optimization methods.

scholarly journals Parameter Estimation Strategies in Thermodynamics

2019 ◽  
Vol 3 (2) ◽  
pp. 56 ◽  
Author(s):  
Johannes Höller ◽  
Patricia Bickert ◽  
Patrick Schwartz ◽  
Martin von Kurnatowski ◽  
Joachim Kerber ◽  
...  
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Numerical Solution ◽  
Satisfactory Result ◽  
Optimization Techniques ◽  
Model Errors ◽  
Thermodynamic Models ◽  
Straightforward Application ◽  
Estimation Problems

Many thermodynamic models used in practice are at least partially empirical and thus require the determination of certain parameters using experimental data. However, due to the complexity of the models involved as well as the inhomogeneity of available data, a straightforward application of basic methods often does not yield a satisfactory result. This work compares three different strategies for the numerical solution of parameter estimation problems, including errors both in the input and in the output variables. Additionally, the new idea to apply multi-criteria optimization techniques to parameter estimation problems is presented. Finally, strategies for the estimation and propagation of the model errors are discussed.

scholarly journals Incremental Parameter Estimation under Rank-Deficient Measurement Conditions

Processes ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 75 ◽  
Author(s):  
Kris Villez ◽  
Julien Billeter ◽  
Dominique Bonvin
Keyword(s):  
Parameter Estimation ◽  
Large Scale ◽  
Model Identification ◽  
Scale Model ◽  
Parameter Estimation Problem ◽  
Data Set ◽  
Large Scale Model ◽  
Estimation Problems ◽  
Important Barrier ◽  
System Partitioning

The computation and modeling of extents has been proposed to handle the complexity of large-scale model identification tasks. Unfortunately, the existing extent-based framework only applies when certain conditions apply. Most typically, it is required that a unique value for each extent can be computed. This severely limits the applicability of this approach. In this work, we propose a novel procedure for parameter estimation inspired by the existing extent-based framework. A key difference with prior work is that the proposed procedure combines structural observability labeling, matrix factorization, and graph-based system partitioning to split the original model parameter estimation problem into parameter estimation problems with the least number of parameters. The value of the proposed method is demonstrated with an extensive simulation study and a study based on a historical data set collected to characterize the isomerization of α -pinene. Most importantly, the obtained results indicate that an important barrier to the application of extent-based frameworks for process modeling and monitoring tasks has been lifted.

scholarly journals Towards cloud-based parallel metaheuristics

2016 ◽  
Vol 32 (5) ◽  
pp. 693-705 ◽  
Author(s):  
Diego Teijeiro ◽  
Xoán C Pardo ◽  
Patricia González ◽  
Julio R Banga ◽  
Ramón Doallo
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Differential Evolution ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Programming Models ◽  
Estimation Model ◽  
Acceptable Result ◽  
Parallel Metaheuristics

Many key problems in science and engineering can be formulated and solved using global optimization techniques. In the particular case of computational biology, the development of dynamic (kinetic) models is one of the current key issues. In this context, the problem of parameter estimation (model calibration) remains as a very challenging task. The complexity of the underlying models requires the use of efficient solvers to achieve adequate results in reasonable computation times. Metaheuristics have been the focus of great consideration as an efficient way of solving hard global optimization problems. Even so, in most realistic applications, metaheuristics require a very large computation time to obtain an acceptable result. Therefore, several parallel schemes have been proposed, most of them focused on traditional parallel programming interfaces and infrastructures. However, with the emergence of cloud computing, new programming models have been proposed to deal with large-scale data processing on clouds. In this paper we explore the applicability of these new models for global optimization problems using as a case study a set of challenging parameter estimation problems in systems biology. We have developed, using Spark, an island-based parallel version of Differential Evolution. Differential Evolution is a simple population-based metaheuristic that, at the same time, is very popular for being very efficient in real function global optimization. Several experiments were conducted both on a cluster and on the Microsoft Azure public cloud to evaluate the speedup and efficiency of the proposal, concluding that the Spark implementation achieves not only competitive speedup against the serial implementation, but also good scalability when the number of nodes grows. The results can be useful for those interested in using parallel metaheuristics for global optimization problems benefiting from the potential of new cloud programming models.

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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