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Title: High-dimensional problems in stochastic modelling of biological processes
Author: Liao, Shuohao
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2017
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Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour 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 behaviour (bifurcation). This thesis addresses such computational challenges by a tensor-structured computational framework. After a background introduction in Chapter 1, Chapter 2 derives the order of convergence in volume size between the stationary distributions of the exact chemical master equation (CME) and its continuous Fokker-Planck approximation (CFPE). It also proposes the multi-scale approaches to address the failure of the CFPE in capturing the noise-induced multi-stability of the CME distribution. Chapter 3 studies the numerical solution of the high-dimensional CFPE using the tensor train and the quantized-TT data formats. In Chapter 4, the tensor solutions are applied to study the parameter estimation, robustness, sensitivity and bifurcation structures of stochastic reaction networks. A Matlab implementation of the proposed methods/algorithms is available at
Supervisor: Erban, Radek ; Maini, Philip K. ; Baker, Ruth E. Sponsor: European Research Council ; Isaac Newton Institute for Mathematical Sciences ; Cambridge ; China Scholarship Council ; EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Tensor Method ; Stochastic Modelling ; High Dimensional Computing