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**Ion, Ion Gabriel ; Wildner, C. ; Loukrezis, D. ; Koeppl, H. ; De Gersem, H.** (2021):

*Tensor-train approximation of the chemical master equation and its application for parameter inference.*

In: The Journal of Chemical Physics, 155 (034102), ISSN 0021-9606,

DOI: 10.1063/5.0045521,

[Article]

## Abstract

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high-dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor-train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction in the computational time is observed as well.

Item Type: | Article |
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Erschienen: | 2021 |

Creators: | Ion, Ion Gabriel ; Wildner, C. ; Loukrezis, D. ; Koeppl, H. ; De Gersem, H. |

Title: | Tensor-train approximation of the chemical master equation and its application for parameter inference |

Language: | English |

Abstract: | In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high-dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor-train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction in the computational time is observed as well. |

Journal or Publication Title: | The Journal of Chemical Physics |

Volume of the journal: | 155 |

Issue Number: | 034102 |

Uncontrolled Keywords: | Numerical linear algebra, Tensor network theory, Bayesian inference, Stochastic processes, Probability theory, Algebraic operation, Chemical reaction dynamics |

Divisions: | 18 Department of Electrical Engineering and Information Technology 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications |

Date Deposited: | 06 Sep 2021 07:11 |

DOI: | 10.1063/5.0045521 |

URL / URN: | https://aip.scitation.org/doi/full/10.1063/5.0045521 |

Additional Information: | 034102 Artikelnummer |

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