Abstract
Individual-based (IB) modelling has been widely used for studying the emergence of complex interactions of bacterial biofilms and their environment. We describe the emulation and calibration of an expensive dynamic simulator of an IB model of microbial communities. We used a combination of multivariate dynamic linear models (DLM) and a Gaussian process to estimate the model parameters of our dynamic emulators. The emulators incorporate a smoothly varying and nonstationary trend that is modelled as a deterministic function of explanatory variables while the Gaussian process (GP) is allowed to capture the remaining intrinsic local variations. We applied this emulation strategy for parameter calibration of a newly developed model for simulation of microbial communities against the iDynoMiCS model. The percentage of variance explained for the four outputs biomass concentration, the total number of particles, biofilm average height and surface roughness range between 84—92% and 97–99% for univariate and multivariate emulators respectively. The simulation-based sensitivity analysis identified carbon substrate, oxygen concentration and maximum specific growth rate for heterotrophic bacteria as the most critical variables for predictions. The calibration results also indicated a general reduction of uncertainty levels in most of the parameters. The study has helped us identify the tradeoff in using different types of models for microbial simulation. The approach illustrated here provides a tractable and computationally efficient technique for calibrating the parameters of an expensive computer model.
Highlights
Individual-based (IB) modelling has been widely used for studying the emergence of complex interactions of bacterial biofilms and their environment
Modularization ensures that emulator parameters are only estimated using only the data from the simulator and not the field or observed data. The advantage of this is that it facilitates the parameter estimation in a computer model calibration because the Markov chain Monte Carlo (MCMC) block is subdivided into two lowerdimensional modules reducing the computational expense
The idea is to calibrate emulators produced by training data from the Newcastle University Frontiers in Engineering Biology (NUFEB) model to synthetic data obtained from the iDynoMiCS
Summary
Individual-based (IB) modelling has been widely used for studying the emergence of complex interactions of bacterial biofilms and their environment. The time-varying autoregressive model is applied to the simulator output to capture the temporal dependence, while the intrinsic random variation of the input space is modelled as a Gaussian process This approach neglected the structural trend of the input data in the model formulation. Our approach extends the work of Liu et al [9] with the incorporation of a smoothly varying and nonstationary trend that is modelled as a deterministic function (e.g. linear or quadratic) and by the Rivers and Boone [2] approach where the Gaussian process is allowed to capture the remaining intrinsic local variations We generalize these approaches to a multivariate problem where we have a matrix-valued time-series of observations.
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