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Tensor Methods for Parameter Estimation and Bifurcation Analysis of Stochastic Reaction Networks

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SDB - Stochastic dynamical systems in biology: numerical methods and applications

Intracellular networks of interacting bio-molecules carry out many essential functions in living cells, but the molecular events underlying the functioning of such networks are ubiquitously random. Stochastic modelling provides an indispensable tool for understanding how cells control, exploit and tolerant the biological noise. A common challenge of stochastic modelling is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviours of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviours (bifurcation). One fundamental reason for these challenges is that the existing computational approaches are susceptible to the curse of dimensionality, i.e., the exponential growth in memory and computational requirements in the dimension (number of species and parameters). Herein, we have developed a tensor-based computational framew  ork to address this computational challenge. It is based on recently proposed low-parametric, separable tensor-structured representations of classical matrices and vectors. The framework covers the whole process from solving the underlying equations to automated parametric analysis of the stochastic models such that the high cost of working in high dimensions is avoided. One notable advantage of the proposed approach lies in its ability to capture all probabilistic information of stochastic models all over the parameter space into one single tensor-formatted solution, in a way that allows linear scaling of basic operations with respect to the number of dimensions. Within such framework, the existing algorithms commonly used in the deterministic framework can be directly used in stochastic models, including parameter inference, robustness analysis, sensitivity analysis, and stochastic bifurcation analysis.

This talk is part of the Isaac Newton Institute Seminar Series series.

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