Statistical emulation as a tool for analysing complex multiscale stochastic biological model outputs

Oyebamiji, Oluwole Kehinde and Wilkinson, D. J. (2016) Statistical emulation as a tool for analysing complex multiscale stochastic biological model outputs. In: VIII International Conference on Sensitivity Analysis of Model Output, 2016-11-30 - 2016-12-03, University of Reunion Island (www.univ-reunion.fr).

Abstract

The performance of credible simulations in open engineered biological frameworks is an important step for practical application of scientific knowledge to solve real-world problems and enhance our ability to make novel discoveries. Therefore, maximising our potential to explore the range of solutions at frontier level could reduce the potential risk of failure on a large scale. One primary application of this type of knowledge is in the management of wastewater treatment systems. Efficient optimisation of wastewater treatment plant focuses on aggregate outcomes of individual particle-level processes. One of the crucial aspects of engineering biology approach in wastewater treatment study is to run a high complex simulation of biological particles. This type of model can scale from one level to another and can also be used to study how to manage real systems effectively with minimal physical experimentation. To identify crucial features and model water treatment plants on a large scale, there is a need to understand the interactions of microbes at fine resolution using models that could provide the best available representation of micro scale responses. The challenge then becomes how we can transfer this small-scale information to the macroscale process in a computationally efficient and sufficiently accurate way. It has been established that the macro scale characteristics of wastewater treatment plants are the consequences of microscale features of a vast number of individual particles that produce the community of such bacterial (Ofiteru et al. 2014). Nevertheless, simulation of open biological systems is challenging because they often involve a large number of bacteria that ranges from order 1012 to 1018 individual particles and are physically complex. The models are computationally expensive and due to computing constraints, limited sets of scenarios are often possible. A simplified approach to this problem is to use a statistical approximation of the simulation ensembles derived from the complex models which will help in reducing the computational burden. Our aim is to build a cheaper surrogate of the Individual- based (IB) model simulation of biological particle. The main issue we address is to highlight the strategy for emulating high-level summaries from the IB model simulation data. Our approach is to condense the massive, long time series outputs of particles of various species by spatially aggregating to produce the most relevant outputs in the form of floc and biofilms aggregates. The data compression has the benefit of suppressing or reducing some of the nonlinear response features, simplifying the construction of the emulator. Some of the most interesting properties at the mesoscale level like the size, shape, and structure of biofilms and flocs are characterised, see Figure 1. For instance, we characterize the floc size using an equivalent diameter. This strategy enables us to treat the flocs as a ball of a sphere and or fractal depending on the shape, and we approximate the diameter of a sphere that circumscribes its boundary or outline.