E. Shcherbakova, S. Matveev, A. Smirnov, E. Tyrtyshnikov
Abstract In the present paper we compare two different iterative approaches to constructing nonnegative tensor train and Tucker decompositions. The first approach is based on idea of alternating projections and randomized sketching for factorization of tensors with nonnegative elements. This approach can be useful for both TT and Tucker formats. The second approach consists of two stages. At the first stage we find the unconstrained tensor train decomposition for the target array. At the second stage we use this initial approximation in order to fix it within moderate number of operations and obtain the factorization with nonnegative factors either in tensor train or Tucker model. We study the performance of these methods for both synthetic data and hyper-spectral image and demonstrate the clear advantage of the latter technique in terms of computational time and wider range of possible applications.
{"title":"Study of performance of low-rank nonnegative tensor factorization methods","authors":"E. Shcherbakova, S. Matveev, A. Smirnov, E. Tyrtyshnikov","doi":"10.1515/rnam-2023-0018","DOIUrl":"https://doi.org/10.1515/rnam-2023-0018","url":null,"abstract":"Abstract In the present paper we compare two different iterative approaches to constructing nonnegative tensor train and Tucker decompositions. The first approach is based on idea of alternating projections and randomized sketching for factorization of tensors with nonnegative elements. This approach can be useful for both TT and Tucker formats. The second approach consists of two stages. At the first stage we find the unconstrained tensor train decomposition for the target array. At the second stage we use this initial approximation in order to fix it within moderate number of operations and obtain the factorization with nonnegative factors either in tensor train or Tucker model. We study the performance of these methods for both synthetic data and hyper-spectral image and demonstrate the clear advantage of the latter technique in terms of computational time and wider range of possible applications.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"231 - 239"},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46211072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation are provided. Performance and convergence of the method are demonstrated on a set of reference problems.
{"title":"Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling","authors":"I. Kapyrin","doi":"10.1515/rnam-2023-0010","DOIUrl":"https://doi.org/10.1515/rnam-2023-0010","url":null,"abstract":"Abstract A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation are provided. Performance and convergence of the method are demonstrated on a set of reference problems.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"115 - 126"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49449819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Liogky, A. Chernyshenko, A. Danilov, Fyodor A. Syomin
Abstract A new parallel numerical framework CarNum is presented for efficient coupling of mathematical models in multiphysics problems such as computational cardiac electromechanics. This framework is based on open source projects, which provide the core functionality of the platform. Computational cardiac electromechanics requires a complex pipeline of solving different types of ordinary and partial differential equations. Our framework allows one to implement different numerical schemes and provides more control in multiphysics coupling. This paper outlines a concept of the new platform and details of numerical modelling of cardiac electromechanics. First experiments with well-known cardiac electromechanics benchmarks show good agreement with other groups and decent parallel scalability.
{"title":"CarNum: parallel numerical framework for computational cardiac electromechanics","authors":"A. Liogky, A. Chernyshenko, A. Danilov, Fyodor A. Syomin","doi":"10.1515/rnam-2023-0011","DOIUrl":"https://doi.org/10.1515/rnam-2023-0011","url":null,"abstract":"Abstract A new parallel numerical framework CarNum is presented for efficient coupling of mathematical models in multiphysics problems such as computational cardiac electromechanics. This framework is based on open source projects, which provide the core functionality of the platform. Computational cardiac electromechanics requires a complex pipeline of solving different types of ordinary and partial differential equations. Our framework allows one to implement different numerical schemes and provides more control in multiphysics coupling. This paper outlines a concept of the new platform and details of numerical modelling of cardiac electromechanics. First experiments with well-known cardiac electromechanics benchmarks show good agreement with other groups and decent parallel scalability.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"127 - 144"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47658149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper presents the dynamical core of the new sea ice model SIMUG (Sea Ice Model on Unstructured Grid) on the A- and CD-types of unstructured triangular grids in the local-element basis on sphere. Three standardized box tests to reproduce the Linear Kinematic Features (LKFs), and the short-term forecast in the real Arctic Ocean geometry with the realistic atmosphere and ocean forcing demonstrate the model quality compared to other sea ice models like CICE, FESOM, MITgcm, and ICON-O. The distinctive features of the model presented are a wide choice of transport schemes, and the new numerical implementation with the serial and parallel C++ coding and INMOST, Ani2D, and Ani3D packages to deal with unstructured grids. Code profiling and scalability assessment are carried out. In general, the A-version of the ice drift model works faster, but has fewer degrees of freedom on the same grid. Due to the increase in the degrees of freedom, the model on the CD grid gives ultra-resolution of LKFs, but requires more strict conditions for stability.
提出了基于球面局部元的A型和cd型非结构化三角形网格海冰模型SIMUG (sea ice model on Unstructured Grid)的动力学核心。与CICE、FESOM、MITgcm和ICON-O等其他海冰模式相比，模拟线性运动特征(LKFs)的三个标准化箱试验和具有真实大气和海洋强迫的真实北冰洋几何形状的短期预报证明了模式的质量。该模型的显著特点是具有广泛的传输方案选择，以及采用串行和并行c++编码和INMOST、Ani2D和Ani3D软件包处理非结构化网格的新数值实现。进行了代码分析和可伸缩性评估。一般来说，a版本的冰漂移模型工作得更快，但在同一网格上的自由度更少。由于自由度的增加，CD网格上的模型给出了LKFs的超分辨率，但对稳定性的要求更严格。
{"title":"SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis","authors":"Sergey S. Petrov, N. Iakovlev","doi":"10.1515/rnam-2023-0012","DOIUrl":"https://doi.org/10.1515/rnam-2023-0012","url":null,"abstract":"Abstract The paper presents the dynamical core of the new sea ice model SIMUG (Sea Ice Model on Unstructured Grid) on the A- and CD-types of unstructured triangular grids in the local-element basis on sphere. Three standardized box tests to reproduce the Linear Kinematic Features (LKFs), and the short-term forecast in the real Arctic Ocean geometry with the realistic atmosphere and ocean forcing demonstrate the model quality compared to other sea ice models like CICE, FESOM, MITgcm, and ICON-O. The distinctive features of the model presented are a wide choice of transport schemes, and the new numerical implementation with the serial and parallel C++ coding and INMOST, Ani2D, and Ani3D packages to deal with unstructured grids. Code profiling and scalability assessment are carried out. In general, the A-version of the ice drift model works faster, but has fewer degrees of freedom on the same grid. Due to the increase in the degrees of freedom, the model on the CD grid gives ultra-resolution of LKFs, but requires more strict conditions for stability.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"145 - 160"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47707361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Simakov, T. Gamilov, F. Liang, P. Chomakhidze, P. Kopylov
Abstract In the present work, we construct a model of coronary flow, which utilizes both CT scans of large coronary arteries and coronary CT perfusion. The model describes pulsatile flow in the patient’s network of coronary vessels and takes into account a number of physiological effects: myocardium contractions, stenoses, impairment of microvascular perfusion. The main novelty of this model is the new smooth boundary conditions that have not been used before in patient-specific simulations of coronary circulation. New boundary conditions use 0D lumped model approach and provide asymptotic convergence of the solution for the cases of one-to-one vascular connection and bifurcation with a very thin child vessel. The new boundary conditions make it possible to estimate the fractional flow margin more accurately. We also studied sensitivity of haemodynamic indices (fractional flow reserve, coronary flow reserve, instantaneous wave-free ratio) to the variations of microcirculation impairment. No substantial difference in sensitivity was observed between new model and original approach. The advantage of the presented approach is the availability of the required data in everyday clinical practice and, thus, improved personalization of the model.
{"title":"Validation of boundary conditions for coronary circulation model based on a lumped parameter approach","authors":"S. Simakov, T. Gamilov, F. Liang, P. Chomakhidze, P. Kopylov","doi":"10.1515/rnam-2023-0013","DOIUrl":"https://doi.org/10.1515/rnam-2023-0013","url":null,"abstract":"Abstract In the present work, we construct a model of coronary flow, which utilizes both CT scans of large coronary arteries and coronary CT perfusion. The model describes pulsatile flow in the patient’s network of coronary vessels and takes into account a number of physiological effects: myocardium contractions, stenoses, impairment of microvascular perfusion. The main novelty of this model is the new smooth boundary conditions that have not been used before in patient-specific simulations of coronary circulation. New boundary conditions use 0D lumped model approach and provide asymptotic convergence of the solution for the cases of one-to-one vascular connection and bifurcation with a very thin child vessel. The new boundary conditions make it possible to estimate the fractional flow margin more accurately. We also studied sensitivity of haemodynamic indices (fractional flow reserve, coronary flow reserve, instantaneous wave-free ratio) to the variations of microcirculation impairment. No substantial difference in sensitivity was observed between new model and original approach. The advantage of the presented approach is the availability of the required data in everyday clinical practice and, thus, improved personalization of the model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"161 - 172"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44818146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Tarasevich, I. Tsybulin, V. A. Onoprienko, D. Kulyamin, E. Volodin
Abstract Modern numerical models of the Earth system are complex and inherit its natural chaotic behaviour. The numerical results depend on various specifications of the simulation process, including computing systems, compilers, etc. Due to the chaotic behaviour, these minor differences lead to significant and unpredictable deviations. Therefore, some procedure verifying that simulation results describe the behaviour of the same physical system is of practical importance. The present paper proposes a statistical verification algorithm developed for the INM RAS Earth system model. Different ensemble generation techniques and statistical estimators are evaluated for verification suitability. The ability of the method to detect the deviations in the simulation results is demonstrated on a series of cases. Practical guidelines on how to choose the perturbation amplitude for the ensemble generation are provided for various verification cases.
{"title":"Ensemble-based statistical verification of INM RAS Earth system model","authors":"M. Tarasevich, I. Tsybulin, V. A. Onoprienko, D. Kulyamin, E. Volodin","doi":"10.1515/rnam-2023-0014","DOIUrl":"https://doi.org/10.1515/rnam-2023-0014","url":null,"abstract":"Abstract Modern numerical models of the Earth system are complex and inherit its natural chaotic behaviour. The numerical results depend on various specifications of the simulation process, including computing systems, compilers, etc. Due to the chaotic behaviour, these minor differences lead to significant and unpredictable deviations. Therefore, some procedure verifying that simulation results describe the behaviour of the same physical system is of practical importance. The present paper proposes a statistical verification algorithm developed for the INM RAS Earth system model. Different ensemble generation techniques and statistical estimators are evaluated for verification suitability. The ability of the method to detect the deviations in the simulation results is demonstrated on a series of cases. Practical guidelines on how to choose the perturbation amplitude for the ensemble generation are provided for various verification cases.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"173 - 186"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49593743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.1515/rnam-2023-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2023-frontmatter3","DOIUrl":"https://doi.org/10.1515/rnam-2023-frontmatter3","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136136003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Tran, V. Shutyaev, H. S. Hoang, Shuai Li, Chinh Kien Nguyen, Hong Phong Nguyen, Thi Thanh Huong Duong
Abstract The present study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden, which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The Neural Network Filter (NNF), proposed in the present paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the NNF is sequential (no batch large assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables. The NNF, developed in the present paper, is a Neural Network Filter (NNF) version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this NNF is that it uses structure of the gain of SEIKF0 taken by the SEIKF at the first time moment of correction process. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed Neural Network SEIKF0 named by NNSEIKF0 makes use of the covariance of a reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the NNSEIKF0 is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation (SPSA) algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF0 and NNSEIKF0, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the NNSEIKF0 and SEIKF0 is given to show the high efficiency of the proposed NNSEIKF0.
{"title":"Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model","authors":"T. Tran, V. Shutyaev, H. S. Hoang, Shuai Li, Chinh Kien Nguyen, Hong Phong Nguyen, Thi Thanh Huong Duong","doi":"10.1515/rnam-2023-0015","DOIUrl":"https://doi.org/10.1515/rnam-2023-0015","url":null,"abstract":"Abstract The present study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden, which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The Neural Network Filter (NNF), proposed in the present paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the NNF is sequential (no batch large assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables. The NNF, developed in the present paper, is a Neural Network Filter (NNF) version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this NNF is that it uses structure of the gain of SEIKF0 taken by the SEIKF at the first time moment of correction process. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed Neural Network SEIKF0 named by NNSEIKF0 makes use of the covariance of a reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the NNSEIKF0 is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation (SPSA) algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF0 and NNSEIKF0, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the NNSEIKF0 and SEIKF0 is given to show the high efficiency of the proposed NNSEIKF0.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"187 - 206"},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42973539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.48550/arXiv.2303.00421
P. Vabishchevich
Abstract The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate when using uniform time grids. When solving applied problems numerically, we should focus on approximations with variable time steps. When using multilevel schemes on non-uniform grids, we should maintain accuracy by choosing appropriate approximations and ensuring stability of the approximate solution. In this paper, we construct unconditionally stable schemes of the first- and second-order accuracy on a non-uniform time grid for the approximate solution of the Cauchy problem for a second-order evolutionary equation. The novelty of the paper consists in the fact that these stability estimates are obtained without any restrictions on the magnitude of the step change and on the number of step changes. We use a special transformation of the original second-order differential-operator equation to a system of first-order equations. For the system of first-order equations, we apply standard two-level time approximations. We obtained stability estimates for the initial data and the right-hand side in finite-dimensional Hilbert space. Eliminating auxiliary variables leads to three-level schemes for the initial second-order evolution equation. Numerical experiments were performed for the test problem for a one-dimensional in space bi-parabolic equation. The accuracy and stability properties of the constructed schemes are demonstrated on non-uniform grids with randomly varying grid steps.
{"title":"Operator-difference schemes on non-uniform grids for second-order evolutionary equations","authors":"P. Vabishchevich","doi":"10.48550/arXiv.2303.00421","DOIUrl":"https://doi.org/10.48550/arXiv.2303.00421","url":null,"abstract":"Abstract The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate when using uniform time grids. When solving applied problems numerically, we should focus on approximations with variable time steps. When using multilevel schemes on non-uniform grids, we should maintain accuracy by choosing appropriate approximations and ensuring stability of the approximate solution. In this paper, we construct unconditionally stable schemes of the first- and second-order accuracy on a non-uniform time grid for the approximate solution of the Cauchy problem for a second-order evolutionary equation. The novelty of the paper consists in the fact that these stability estimates are obtained without any restrictions on the magnitude of the step change and on the number of step changes. We use a special transformation of the original second-order differential-operator equation to a system of first-order equations. For the system of first-order equations, we apply standard two-level time approximations. We obtained stability estimates for the initial data and the right-hand side in finite-dimensional Hilbert space. Eliminating auxiliary variables leads to three-level schemes for the initial second-order evolution equation. Numerical experiments were performed for the test problem for a one-dimensional in space bi-parabolic equation. The accuracy and stability properties of the constructed schemes are demonstrated on non-uniform grids with randomly varying grid steps.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"267 - 277"},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46700237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature (cell motility, virus diffusion, intracellular virus replication). Intracellular replication model is based on a Markov chain with time-inhomogeneous propensities that depend on the extracellular level of virions. Reaction diffusion equations used to model free virion diffusion in the lymphoid tissue have moving sources, which are determined by the positions of the infected cells (immune cell motility model) and the rate of virion secretion from them (intracellular model). Immune cell motility model parameterizes the intercellular interaction forces, friction and the stochastic force of active cell motility. Together, this allows for a proper description of the intracellular stochasticity that propagates across multiple scales. A hybrid discrete-continuous stochastic-deterministic algorithm for simulation of the multiscale model based on the uniformization Monte Carlo method is implemented.
{"title":"Computational methods for multiscale modelling of virus infection dynamics","authors":"D. Grebennikov","doi":"10.1515/rnam-2023-0007","DOIUrl":"https://doi.org/10.1515/rnam-2023-0007","url":null,"abstract":"Abstract Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature (cell motility, virus diffusion, intracellular virus replication). Intracellular replication model is based on a Markov chain with time-inhomogeneous propensities that depend on the extracellular level of virions. Reaction diffusion equations used to model free virion diffusion in the lymphoid tissue have moving sources, which are determined by the positions of the infected cells (immune cell motility model) and the rate of virion secretion from them (intracellular model). Immune cell motility model parameterizes the intercellular interaction forces, friction and the stochastic force of active cell motility. Together, this allows for a proper description of the intracellular stochasticity that propagates across multiple scales. A hybrid discrete-continuous stochastic-deterministic algorithm for simulation of the multiscale model based on the uniformization Monte Carlo method is implemented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"75 - 87"},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49427510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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