Neural Stochastic Delay Differential Equations for Astronomical Time Series Classification and Novelty Detection

Abstract

Fundamental difficulties in astronomical research arise from irregular sampling and incomplete time series data, especially when working with datasets from large-scale surveys such as the Large Synoptic Survey Telescope (LSST). In order to tackle the crucial tasks of classification and novelty detection in astrophysical data analysis, we suggest a novel mathematical framework based on Neural Stochastic Delay Differential Equations (Neural SDDEs). Our method combines stochastic delay differential equations with neural networks, where the neural component explicitly accounts for time delays in the underlying dynamics while learning the drift coefficients. The framework includes mechanisms to deal with irregular temporal sampling, a numerical solver for the resulting stochastic system, and a neural network architecture for learning SDDE parameters. Using astronomical time series data that is irregularly sampled, we assess the model's performance on classification tasks. The outcomes show that even when there are temporal irregularities in the observations, the model can still maintain classification accuracy. Furthermore, we use our framework to detect anomalous astrophysical events for novelty detection when the labels are not complete. By providing improvements in classification and anomaly detection capabilities over current techniques, this work establishes Neural SDDEs as a mathematically principled method for analyzing astronomical time series impacted by observational constraints.