Emulating dynamic non-linear simulators using Gaussian processes

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and Van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability

A Distributed and Privacy-Aware Speed Advisory System for Optimising Conventional and Electric Vehicles Networks

One of the key ideas to make Intelligent Transportation Systems (ITS) work effectively is to deploy advanced communication and cooperative control technologies among the vehicles and road infrastructures. In this spirit, we propose a consensus-based distributed speed advisory system that optimally determines a recommended common speed for a given area in order that the group emissions, or group battery consumptions, are minimised. Our algorithms achieve this in a privacy-aware manner; namely, individual vehicles do not reveal in-vehicle information to other vehicles or to infrastructure. A mobility simulator is used to illustrate the efficacy of the algorithm, and hardware-in-the-loop tests involving a real vehicle are given to illustrate user acceptability and ease of the deployment.Comment: This is a journal paper based on the conference paper "Highway speed limits, optimised consensus, and intelligent speed advisory systems" presented at the 3rd International Conference on Connected Vehicles and Expo (ICCVE 2014) in November 2014. This is the revised version of the paper recently submitted to the IEEE Transactions on Intelligent Transportation Systems for publicatio

Data-driven Flood Emulation: Speeding up Urban Flood Predictions by Deep Convolutional Neural Networks

Computational complexity has been the bottleneck of applying physically-based simulations on large urban areas with high spatial resolution for efficient and systematic flooding analyses and risk assessments. To address this issue of long computational time, this paper proposes that the prediction of maximum water depth rasters can be considered as an image-to-image translation problem where the results are generated from input elevation rasters using the information learned from data rather than by conducting simulations, which can significantly accelerate the prediction process. The proposed approach was implemented by a deep convolutional neural network trained on flood simulation data of 18 designed hyetographs on three selected catchments. Multiple tests with both designed and real rainfall events were performed and the results show that the flood predictions by neural network uses only 0.5 % of time comparing with physically-based approaches, with promising accuracy and ability of generalizations. The proposed neural network can also potentially be applied to different but relevant problems including flood predictions for urban layout planning