Learning chemical reaction networks from trajectory data

Wei Zhang; Stefan Klus; Tim Conrad; Christof Schütte

doi:10.1137/19M1265880

Learning chemical reaction networks from trajectory data

Wei Zhang
, Stefan Klus
, Tim Conrad
, Christof Schütte

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l¹ sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.

Original language	English
Pages (from-to)	2000-2046
Number of pages	47
Journal	SIAM Journal on Applied Dynamical Systems
Volume	18
Issue number	4
DOIs	https://doi.org/10.1137/19M1265880
Publication status	Published - 2019

Keywords

Asymptotic analysis
Chemical reactions
Data-driven methods
Inverse problems
L sparse optimization

ASJC Scopus subject areas

Analysis
Modelling and Simulation

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10.1137/19M1265880

Cite this

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title = "Learning chemical reaction networks from trajectory data",

abstract = "We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.",

keywords = "Asymptotic analysis, Chemical reactions, Data-driven methods, Inverse problems, L sparse optimization",

author = "Wei Zhang and Stefan Klus and Tim Conrad and Christof Sch{\"u}tte",

note = "Funding Information: ∗Received by the editors June 3, 2019; accepted for publication (in revised form) by L. Deville September 24, 2019; published electronically November 12, 2019. https://doi.org/10.1137/19M1265880 Funding: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy, the Berlin Mathematics Research Center, MATH+ (EXC-2046/1, project 390685689), and the Einstein Center of Mathematics (ECMath) through project CH21. †Zuse Institute Berlin, D-14195 Berlin, Germany ([email protected], [email protected], [email protected]). ‡Department of Mathematics and Computer Science, Freie Universit{\"a}t Berlin, D-14195 Berlin, Germany ([email protected]). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics",

year = "2019",

doi = "10.1137/19M1265880",

language = "English",

volume = "18",

pages = "2000--2046",

journal = "SIAM Journal on Applied Dynamical Systems",

issn = "1536-0040",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

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TY - JOUR

T1 - Learning chemical reaction networks from trajectory data

AU - Zhang, Wei

AU - Klus, Stefan

AU - Conrad, Tim

AU - Schütte, Christof

N1 - Funding Information: ∗Received by the editors June 3, 2019; accepted for publication (in revised form) by L. Deville September 24, 2019; published electronically November 12, 2019. https://doi.org/10.1137/19M1265880 Funding: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy, the Berlin Mathematics Research Center, MATH+ (EXC-2046/1, project 390685689), and the Einstein Center of Mathematics (ECMath) through project CH21. †Zuse Institute Berlin, D-14195 Berlin, Germany ([email protected], [email protected], [email protected]). ‡Department of Mathematics and Computer Science, Freie Universität Berlin, D-14195 Berlin, Germany ([email protected]). Publisher Copyright: © 2019 Society for Industrial and Applied Mathematics

PY - 2019

Y1 - 2019

N2 - We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.

AB - We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.

KW - Asymptotic analysis

KW - Chemical reactions

KW - Data-driven methods

KW - Inverse problems

KW - L sparse optimization

UR - https://www.scopus.com/pages/publications/85077741033

U2 - 10.1137/19M1265880

DO - 10.1137/19M1265880

M3 - Article

AN - SCOPUS:85077741033

SN - 1536-0040

VL - 18

SP - 2000

EP - 2046

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

IS - 4

ER -

Learning chemical reaction networks from trajectory data

Abstract

Keywords

ASJC Scopus subject areas

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