GAUSSIAN-PROCESS MODELS OF POPULATION DYNAMICS

Surrogate models of population dynamics are crucial for ensemble-based computations such as data assimilation, uncertainty quantification, and optimal design. One such surrogate is a data-driven Gaussian process (GP) that respects natural physical constraints. Our approach leverages output transformation and variational inference to ensure physical admissibility of the population variable. It also employs statistical learning and kernel discovery algorithms to identify GP structures that achieve metric-based optimal fitting or prediction of the measured population data under different environmental conditions. We examine the impact of different metrics on the resulting optimal kernels and propose an adaptive beam search method for efficient identification of such kernels. The efficacy of the GP models is demonstrated through numerical experiments with a dataset describing the evolution of a mosquito population. The proposed framework can be applied and extended to a wide range of biological systems, paving the way for uncertainty-informed decision making and real-time data generation.