Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

The exponential growth of astronomical time-series data from missions such as Kepler, TESS, and LSST has created an urgent need for statistical frameworks capable of providing both scalability and interpretability. Gaussian Processes (GPs) have emerged as a powerful tool for probabilistic modeling due to their ability to capture correlated structures and quantify uncertainty. However, their computational complexity, which scales cubically with dataset size, has limited their applicability to large-scale astronomical datasets. This paper introduces a novel Gaussian Process framework, termed celerite, which achieves exact and efficient inference for one-dimensional time-series data. The proposed method exploits the semiseparable structure of covariance matrices derived from mixtures of exponential kernels, reducing computational complexity from O(N 3 ) to O(N). Unlike traditional sparse or approximate GP methods, celerite maintains full model fidelity while enabling rapid processing of datasets containing millions of observations. Experimental evaluations on both simulated and real-world stellar light curves demonstrate that the proposed model accurately captures quasi-periodic and oscillatory variability with minimal loss of precision. The framework’s physical interpretability, numerical stability, and linear scalability make it highly suitable for modern astronomical pipelines and timedomain analyses. Beyond astrophysics, the principles of the celerite approach hold promise for other domains requiring fast, interpretable, and probabilistic time-series modeling.