Scalable Weak Constraint Gaussian Processes

A Weak Constraint Gaussian Process (WCGP) model is presented to integrate noisy inputs into the classical Gaussian Process predictive distribution. This 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 prove that the parallel implementation preserves the accuracy of the sequential one. The algorithm's scalability is further proved to be O(p(2)) where p is the number of processors.