Abstract
We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization–based framework for parameter estimation in coupled chaotic systems with some state–of–the–art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non–parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC–based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of “populations”, i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.
Highlights
Most dynamical systems studied in the physical, biological and social sciences that exhibit a rich dynamical behavior can be modeled by sets of nonlinear differential equations
In this paper we investigate techniques that combine a synchronization–based framework for parameter estimation in coupled chaotic systems with some state–of–the–art computational inference methods borrowed from the recent literature in computational statistics
Accelerated Random Search We first focus on a parameter estimation method for chaotic intercellular networks that takes advantage of chaos synchronization and is based on an efficient Monte Carlo optimization procedure, known as accelerated random search (ARS) method [29,31]
Summary
Most dynamical systems studied in the physical, biological and social sciences that exhibit a rich dynamical behavior can be modeled by sets of nonlinear differential equations. These mathematical models are a useful tool to predict complex behaviors using numerical simulations. The problem of parameter estimation can be tackled in different ways, e.g., using multiple shooting methods [6,7,8] or some statistical procedures based on time discretizations and other approximations [9,10,11,12,13]. These methods involve the solution of high-dimensional minimization problems, since the unknown parameters and the initial values of the trajectory segments between the sampling times need to be estimated [7,14]
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