Weak Constraint Gaussian Processes for optimal sensor placement

We present a Weak Constraint Gaussian Process (WCGP) model to integrate noisy inputs into the classical Gaussian Process (GP) predictive distribution. This model follows a Data Assimilation approach (i.e. by considering information provided by observed values of a noisy input in a time window). Due to the increased number of states processed from real applications and the time complexity of GP algorithms, the problem mandates a solution in a high performance computing environment. In this paper, parallelism is explored by defining the parallel WCGP model based on domain decomposition. Both a mathematical formulation of the model and a parallel algorithm are provided. We use the algorithm for an optimal sensor placement problem. Experimental results are provided for pollutant dispersion within a real urban environment.