Parameter inference for stochastic biological models

PhD ThesisParameter inference is the field concerned with estimating reliable model parameters from data. In recent years there has been a trend in the biology community toward single cell technologies such as fluorescent flow cytometry, transcriptomics and mass cytometry: providing a rich array of stochastic time series and temporal distribution data for analysis. Deterministically, there are a wide range of parameter inference and global optimisation techniques available. However, these do not always scale well to non-deterministic (i.e., stochastic) settings — whereby the temporal evolution of the system can be described by a chemical master equation for which the solution is nearly always intractable, and the dynamic behaviour of a system is hard to predict. For systems biology, the inference of stochastic parameters remains a bottleneck for accurate model simulation. This thesis is concerned with the parameter inference problem for stochastic chemical reaction networks. Stochastic chemical reaction networks are most frequently modelled as a continuous time discretestate Markov chain using Gillespie’s stochastic simulation algorithm. Firstly, I present a new parameter inference algorithm, SPICE, that combines Gillespie’s algorithm with the cross-entropy method. The cross-entropy method is a novel approach for global optimisation inspired from the field of rare-event probability estimation. I then present recent advances in utilising the generalised method of moments for inference, and seek to provide these approaches with a direct stochastic simulation based correction. Subsequently, I present a novel use of a recent multi-level tau-leaping approach for simulating population moments efficiently, and use this to provide a simulation based correction to the generalised method of moments. I also propose a new method for moment closures based on the use of Padé approximants. The presented algorithms are evaluated on a number of challenging case studies, including bistable systems — e.g., the Schlögl System and the Genetic Toggle Switch — and real experimental data. Experimental results are presented using each of the given algorithms. We also consider ‘realistic’ data — i.e., datasets missing model species, multiple datasets originating from experiment repetitions, and datasets containing arbitrary units (e.g., fluorescence values). The developed approaches are found to be viable alternatives to existing state-ofthe-art methods, and in certain cases are able to outperform other methods in terms of either speed, or accuracyNewcastle/Liverpool/Durham BBSRC Doctoral Training Partnership for financial suppor

Krylov Subspace Model Order Reduction for Nonlinear and Bilinear Control Systems

The use of Krylov subspace model order reduction for nonlinear/bilinear systems, over the past few years, has become an increasingly researched area of study. The need for model order reduction has never been higher, as faster computations for control, diagnosis and prognosis have never been higher to achieve better system performance. Krylov subspace model order reduction techniques enable this to be done more quickly and efficiently than what can be achieved at present. The most recent advances in the use of Krylov subspaces for reducing bilinear models match moments and multimoments at some expansion points which have to be obtained through an optimisation scheme. This therefore removes the computational advantage of the Krylov subspace techniques implemented at an expansion point zero. This thesis demonstrates two improved approaches for the use of one-sided Krylov subspace projection for reducing bilinear models at the expansion point zero. This work proposes that an alternate linear approximation can be used for model order reduction. The advantages of using this approach are improved input-output preservation at a simulation cost similar to some earlier works and reduction of bilinear systems models which have singular state transition matrices. The comparison of the proposed methods and other original works done in this area of research is illustrated using various examples of single input single output (SISO) and multi input multi output (MIMO) models

Resilience-oriented control and communication framework for cyber-physical microgrids

Climate change drives the energy supply transition from traditional fossil fuel-based power generation to renewable energy resources. This transition has been widely recognised as one of the most significant developing pathways promoting the decarbonisation process toward a zero-carbon and sustainable society. Rapidly developing renewables gradually dominate energy systems and promote the current energy supply system towards decentralisation and digitisation. The manifestation of decentralisation is at massive dispatchable energy resources, while the digitisation features strong cohesion and coherence between electrical power technologies and information and communication technologies (ICT). Massive dispatchable physical devices and cyber components are interdependent and coupled tightly as a cyber-physical energy supply system, while this cyber-physical energy supply system currently faces an increase of extreme weather (e.g., earthquake, flooding) and cyber-contingencies (e.g., cyberattacks) in the frequency, intensity, and duration. Hence, one major challenge is to find an appropriate cyber-physical solution to accommodate increasing renewables while enhancing power supply resilience. The main focus of this thesis is to blend centralised and decentralised frameworks to propose a collaboratively centralised-and-decentralised resilient control framework for energy systems i.e., networked microgrids (MGs) that can operate optimally in the normal condition while can mitigate simultaneous cyber-physical contingencies in the extreme condition. To achieve this, we investigate the concept of "cyber-physical resilience" including four phases, namely prevention/upgrade, resistance, adaption/mitigation, and recovery. Throughout these stages, we tackle different cyber-physical challenges under the concept of microgrid ranging from a centralised-to-decentralised transitional control framework coping with cyber-physical out of service, a cyber-resilient distributed control methodology for networked MGs, a UAV assisted post-contingency cyber-physical service restoration, to a fast-convergent distributed dynamic state estimation algorithm for a class of interconnected systems.Open Acces

Automatic Extraction of Ordinary Differential Equations from Data: Sparse Regression Tools for System Identification

Studying nonlinear systems across engineering, physics, economics, biology, and chemistry often hinges upon successfully discovering their underlying dynamics. However, despite the abundance of data in today's world, a complete comprehension of these governing equations often remains elusive, posing a significant challenge. Traditional system identification methods for building mathematical models to describe these dynamics can be time-consuming, error-prone, and limited by data availability. This thesis presents three comprehensive strategies to address these challenges and automate model discovery. The procedures outlined here employ classic statistical and machine learning methods, such as signal filtering, sparse regression, bootstrap sampling, Bayesian inference, and unsupervised learning algorithms, to capture complex and nonlinear relationships in data. Building on these foundational techniques, the proposed processes offer a reliable and efficient approach to identifying models of ordinary differential equations from data, differing from and complementing existing frameworks. The results presented here provide rigorous benchmarking against state-of-the-art algorithms, demonstrating the proposed methods' effectiveness in model discovery and highlighting the potential for discovering governing equations across applications such as weather forecasting, chemical reaction and electrical circuit modelling, and predator-prey dynamics. These methods can aid in solving critical decision-making problems, including optimising resource allocation, predicting system failures, and facilitating adaptive control in various domains. Ultimately, the strategies developed in this thesis are designed to integrate seamlessly into current workflows, thereby promoting data-driven decision-making and enhancing understanding of complex system dynamics

Neural Model-Based Advanced Control of Chylla-Haase Reactor

The objective of this thesis is to develop advanced control method and to design advanced control system for the polymerization reactor (Chylla-Haase) to maintain the high accurate reactor temperature. The first stage of this research start with the development of mathematical model of the process. The sub-models for monomer concentration, polymerization rate, reactor temperature and jacket outlet/inlet temperature are developed and implemented in Matlab/Simulink. Four conventional control methods were applied to the reactor: a Proportional –Integral-Derivative (PID), Cascade control (CCs), Linear-Quadratic-Regulator (LQR), and Linear model predictive control (LMPC). The simulation results show that the PID controller is unable to perform satisfactorily due to the change of physical properties unless constant re-tuning takes place. Also, Cascade Control the most common control method used in such processes cannot guarantee a robust performance under varying disturbance and system uncertainty. In addition, LQR and linear MPC methods lead to better results compared with the previous two methods. But it is still under an assumption of the linearized plant. Three advanced neural network based control schemes are also proposed in this thesis: radial basis function RBF neural network inverse model based feedforward-feedback control scheme, RBF based model predictive control and multi-layer perception (MLP) based model predictive control. The major objective of these control schemes is to maintain the reactor temperature within its tolerance range under disturbances and system uncertainty. Satisfactory control performance in terms of effective regulation and robustness to disturbance have been achieved. In the feedforward-feedback control scheme, a neural network model is used to predict reactor temperature. Then, a neural network inverse model is used to estimate the valve position of the reactor, the manipulated variable. This method can identify the controlled system with the RBF neural network identifier. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance. These advanced methods achieved the much improved control performance compared with conventional control schemes. The main contribution of this research lies in the following aspects. The MPC theory is realised to control Chylla-Haase polymerization reactor. Two adaptive reactor models including the RBF network model and MLP model are developed to predict the multiple-step-ahead values of the reactor output. Their modelling ability is compared with that of the models with fixed parameters and proven to be better. The RBF neural network and the MLP is trained by the recursive Least Squares (RLS) algorithm and is used to model parameter uncertainty in nonlinear dynamics of the Chylla-Haase reactor. The predictive control strategy based on the RBF neural network is applied to achieve set-point tracking of the reactor output against disturbances. The result shows that the RBF based model predictive control gives reliable result in the presence of some disturbances and keeps the reactor temperature within a tight tolerance range around the specified reaction temperature. Moreover, RBF neural network based model predictive control strategy has also been used to reduce the batch time in order to shorten the reaction period. RBF neural network is considered as a prediction model for control purpose which is based to minimize a cost function in order to determine an optimal sequence of control moves. The result shows that the RBF based model predictive control gives reliable result in the presence of variation of monomer and presence of some disturbances for keeping the reactor temperature within a tight tolerance range around the specified reaction temperature without harming the quality of the temperature control

Adaptive techniques in signal processing and connectionist models

This thesis covers the development of a series of new methods and the application of adaptive filter theory which are combined to produce a generalised adaptive filter system which may be used to perform such tasks as pattern recognition. Firstly, the relevant background adaptive filter theory is discussed in Chapter 1 and methods and results which are important to the rest of the thesis are derived or referenced. Chapter 2 of this thesis covers the development of a new adaptive algorithm which is designed to give faster convergence than the LMS algorithm but unlike the Recursive Least Squares family of algorithms it does not require storage of a matrix with n2 elements, where n is the number of filter taps. In Chapter 3 a new extension of the LMS adaptive notch filter is derived and applied which gives an adaptive notch filter the ability to lock and track signals of varying pitch without sacrificing notch depth. This application of the LMS filter is of interest as it demonstrates a time varying filter solution to a stationary problem. The LMS filter is next extended to the multidimensional case which allows the application of LMS filters to image processing. The multidimensional filter is then applied to the problem of image registration and this new application of the LMS filter is shown to have significant advantages over current image registration methods. A consideration of the multidimensional LMS filter as a template matcher and pattern recogniser is given. In Chapter 5 a brief review of statistical pattern recognition is given, and in Chapter 6 a review of relevant connectionist models. In Chapter 7 the generalised adaptive filter is derived. This is an adaptive filter with the ability to model non-linear input-output relationships. The Volterra functional analysis of non-linear systems is given and this is combined with adaptive filter methods to give a generalised non-linear adaptive digital filter. This filter is then considered as a linear adaptive filter operating in a non-linearly extended vector space. This new filter is shown to have desirable properties as a pattern recognition system. The performance and properties of the new filter is compared with current connectionist models and results demonstrated in Chapter 8. In Chapter 9 further mathematical analysis of the networks leads to suggested methods to greatly reduce network complexity for a given problem by choosing suitable pattern classification indices and allowing it to define its own internal structure. In Chapter 10 robustness of the network to imperfections in its implementation is considered. Chapter 11 finishes the thesis with some conclusions and suggestions for future work.Science and Engineering Research Council; Dr W. Fitzgerald; Marconi