Model Reduction for Kinetic Models of Biological Systems
High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to redu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/5/863 |
| _version_ | 1797567086464073728 |
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| author | Neveen Ali Eshtewy Lena Scholz |
| author_facet | Neveen Ali Eshtewy Lena Scholz |
| author_sort | Neveen Ali Eshtewy |
| collection | DOAJ |
| description | High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions. |
| first_indexed | 2024-03-10T19:36:36Z |
| format | Article |
| id | doaj.art-6cadc85790e64f11b2ba8d1ecfa243e0 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:36:36Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6cadc85790e64f11b2ba8d1ecfa243e02023-11-20T01:36:46ZengMDPI AGSymmetry2073-89942020-05-0112586310.3390/sym12050863Model Reduction for Kinetic Models of Biological SystemsNeveen Ali Eshtewy0Lena Scholz1Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, GermanyDepartment of Mathematics, Technische Universität Berlin, 10623 Berlin, GermanyHigh dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions.https://www.mdpi.com/2073-8994/12/5/863model reductionsingular value decompositionproper orthogonal methoddiscrete empirical interpolation methodkinetic modelingsystems biology |
| spellingShingle | Neveen Ali Eshtewy Lena Scholz Model Reduction for Kinetic Models of Biological Systems Symmetry model reduction singular value decomposition proper orthogonal method discrete empirical interpolation method kinetic modeling systems biology |
| title | Model Reduction for Kinetic Models of Biological Systems |
| title_full | Model Reduction for Kinetic Models of Biological Systems |
| title_fullStr | Model Reduction for Kinetic Models of Biological Systems |
| title_full_unstemmed | Model Reduction for Kinetic Models of Biological Systems |
| title_short | Model Reduction for Kinetic Models of Biological Systems |
| title_sort | model reduction for kinetic models of biological systems |
| topic | model reduction singular value decomposition proper orthogonal method discrete empirical interpolation method kinetic modeling systems biology |
| url | https://www.mdpi.com/2073-8994/12/5/863 |
| work_keys_str_mv | AT neveenalieshtewy modelreductionforkineticmodelsofbiologicalsystems AT lenascholz modelreductionforkineticmodelsofbiologicalsystems |