scholarly journals Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ1-regularization

2020 ◽  
Vol 30 (5) ◽  
pp. 053122
Author(s):  
Q. Yang ◽  
C. A. Sing-Long ◽  
E. J. Reed
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Chemical Reaction ◽  
Nonlinear Dynamical Systems ◽  
Chemical Reaction Networks ◽  
Data Driven ◽  
Reaction Networks ◽  
Nonlinear Dynamical ◽  
ℓ1 Regularization

scholarly journals Multidimensional Approximation of Nonlinear Dynamical Systems

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Patrick Gelß ◽  
Stefan Klus ◽  
Jens Eisert ◽  
Christof Schütte
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Data Driven ◽  
High Dimensional ◽  
Data Sets ◽  
Nonlinear Dynamical ◽  
Tensor Network ◽  
Wide Range ◽  
Multidimensional Approximation

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.

scholarly journals Inferring reaction network structure from single-cell, multiplex data, using toric systems theory

2019 ◽  
Author(s):  
Shu Wang ◽  
Jia-Ren Lin ◽  
Eduardo D. Sontag ◽  
Peter K. Sorger
Keyword(s):  
Single Cell ◽  
Chemical Reaction ◽  
Network Structure ◽  
Statistical Models ◽  
Control Cell ◽  
Toric Varieties ◽  
Chemical Reaction Networks ◽  
Data Driven ◽  
Cell Subpopulation ◽  
Reaction Networks

AbstractThe goal of many single-cell studies on eukaryotic cells is to gain insight into the biochemical reactions that control cell fate and state. In this paper we introduce the concept of effective stoichiometric space (ESS) to guide the reconstruction of biochemical networks from multiplexed, fixed time-point, single-cell data. In contrast to methods based solely on statistical models of data, the ESS method leverages the power of the geometric theory of toric varieties to begin unraveling the structure of chemical reaction networks (CRN). This application of toric theory enables a data-driven mapping of covariance relationships in single cell measurements into stoichiometric information, one in which each cell subpopulation has its associated ESS interpreted in terms of CRN theory. In the development of ESS we reframe certain aspects of the theory of CRN to better match data analysis. As an application of our approach we process cytomery- and image-based single-cell datasets and identify differences in cells treated with kinase inhibitors. Our approach is directly applicable to data acquired using readily accessible experimental methods such as Fluorescence Activated Cell Sorting (FACS) and multiplex immunofluorescence.Author summaryWe introduce a new notion, which we call the effective stoichiometric space (ESS), that elucidates network structure from the covariances of single-cell multiplexed data. The ESS approach differs from methods that are based on purely statistical models of data: it allows a completely new and data-driven translation of the theory of toric varieties in geometry and specifically their role in chemical reaction networks (CRN). In the process, we reframe certain aspects of the theory of CRN. As illustrations of our approach, we find stoichiometry in different single-cell datasets, and pinpoint dose-dependence of network perturbations in drug-treated cells.

scholarly journals On sparse identification of complex dynamical systems: A study on discovering influential reactions in chemical reaction networks

Fuel ◽  
2020 ◽  
Vol 279 ◽  
pp. 118204
Author(s):  
Farshad Harirchi ◽  
Doohyun Kim ◽  
Omar Khalil ◽  
Sijia Liu ◽  
Paolo Elvati ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Complex Dynamical Systems

A data-driven approach to model calibration for nonlinear dynamical systems

2019 ◽  
Vol 125 (24) ◽  
pp. 244901 ◽  
Author(s):  
C. M. Greve ◽  
K. Hara ◽  
R. S. Martin ◽  
D. Q. Eckhardt ◽  
J. W. Koo
Keyword(s):  
Dynamical Systems ◽  
Model Calibration ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Data Driven Approach
Sign in / Sign up

Export Citation Format

Share Document