[SS04] Dynamics and Structures of Biological Networks I: Chemical Reaction Networks

[SS04-02] Sparse Spectral Estimation of the Koopman Operator Reveals Key Insights into the Dynamics of Stochastic Reaction Networks

*Ankit Gupta¹, Mustafa Khammash¹ (1. ETH Zürich (Switzerland))

Keywords:

Reaction Networks,Markov Chain models,Koopman Operator,Sensitivity Analysis,Spectral Methods

Intracellular reaction networks are often characterized by stochastic dynamics, typically modeled as continuous-time Markov chains (CTMCs). However, computational analyses of these models—aimed at investigating the dynamics of the underlying networks—remains challenging due to the inherent curse of dimensionality. In this talk, I will present a recent method we developed for estimating the stochastic Koopman operator associated with a given network. By providing a sparse spectral representation of the operator, our approach circumvents many of the computational bottlenecks typically encountered. Moreover, this representation makes it straightforward to infer key dynamical characteristics—such as parameter sensitivities and spectral densities—thereby offering deeper insights into the behavior of stochastic reaction networks.