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Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equations

YongKyung Oh, Seungsu Kam, Dong-Young Lim, Sungil Kim

Abstract

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential Equations (Neural SDDEs) that combines stochastic modeling with neural networks to capture delayed temporal dynamics and handle irregular observations. Our approach integrates a delay-aware neural architecture, a numerical solver for SDDEs, and mechanisms to robustly learn from noisy, sparse sequences. Experiments on irregularly sampled astronomical data demonstrate strong classification accuracy and effective detection of novel astrophysical events, even with partial labels. This work highlights Neural SDDEs as a principled and practical tool for time series analysis under observational constraints.

Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equations

Abstract

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential Equations (Neural SDDEs) that combines stochastic modeling with neural networks to capture delayed temporal dynamics and handle irregular observations. Our approach integrates a delay-aware neural architecture, a numerical solver for SDDEs, and mechanisms to robustly learn from noisy, sparse sequences. Experiments on irregularly sampled astronomical data demonstrate strong classification accuracy and effective detection of novel astrophysical events, even with partial labels. This work highlights Neural SDDEs as a principled and practical tool for time series analysis under observational constraints.

Paper Structure

This paper contains 16 sections, 16 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Proposed Neural SDDE
  5. Initial value choice.
  6. Modeling Path-Dependency with Delayed States and Control Paths
  7. Adjoint Method for Our Neural SDDE
  8. Forward Pass (SDDE Integration).
  9. Adjoint Variable and Backward Pass.
  10. Experiment
  11. Dataset
  12. Comparative Scenarios
  13. Benchmark methods
  14. Performance Comparisons
  15. Sensitivity Analysis on Delay Parameter
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Illustration of the Neural SDDE learning process. The dashed line represents the unknown temporal dynamics, observed only at sparse and irregular time points (dots). The model infers a continuous latent trajectory (solid line) governed by the Neural SDDE. Using past observations (highlighted window), the model learns the dynamics from incomplete data by capturing delayed and stochastic dependencies.
  • Figure 1: Class distribution
  • Figure 2: Performance comparison of various models across different experimental scenarios (Average and standard deviation of five iterations for each scenario. $\tau$ is 3 for Neural DDE, SDE-Delay-Net and the proposed Neural SDDE.)
  • Figure 3: Sensitivity analysis with $\tau$