Imene R. Goumiri, Lawrence Livermore National Laboratory; Alec M. Dunton, Lawrence Livermore National Laboratory; Amanda L. Muyskens, Lawrence Livermore National Laboratory; Benjamin W. Priest, Lawrence Livermore National Laboratory; Robert E. Armstrong, Lawrence Livermore National Laboratory
Keywords: Light curves, Gaussian Processes
Abstract:
Temporal variations of apparent magnitude, called light curves, are observational statistics of interest captured by optical telescopes. These light curves are time series of the color and brightness of resident space objects over long periods.
Light curves afford the exploration of Space domain Awareness (SDA) objectives such as object identification or pose estimation as latent variable inference problems while remaining inexpensive to collect compared to higher fidelity observations requiring high precision instruments. However, sky noise and weather introduce photometric catalog noise and limited sensor availability can produce gappy time-series. These external factors confound the automated exploitation of light curves, which makes light curves completion a crucial problem for applications. Traditionally, image or time-series completion problems have been approached with diffusion-based or exemplar-based methods. More recently, Deep Neural Networks (DNNs) have become the tool of choice due to their empirical success at learning complex nonlinear embeddings. However, DNNs often require large training data that are not necessarily available when looking at unique features of a light curve of a single satellite.
In this paper, we present a novel approach to predicting missing and future data points of light curves using Gaussian Processes (GPs). GPs are non-linear probabilistic models that infer posterior distributions over functions and naturally quantify uncertainty. However, the cubic scaling of GP inference and training is a major barrier to their adoption in applications. In particular, a single longitudinal light curve can feature hundreds of thousands of observations, which is well beyond the practical realization limits of a conventional GP on a single machine. Consequently, we employ MuyGPs, a scalable framework for hyperparameter estimation of GP models that uses nearest neighbors sparsification and local cross-validation. MuyGPs allows us to quickly train models on light curve data in seconds on a single workstation. In this manuscript we explore light curve completion and forecasting, and compare embeddings of the light curve data into multi-dimensional spaces to take advantage of daily and yearly periodicity. We show that our method outperforms feedforward DNNs both in terms of accuracy and quantity of training data required.
Date of Conference: September 27-20, 2022
Track: Machine Learning for SSA Applications