SELDON: Supernova Explosions Learned by Deep ODE Networks

Jiezhong Wu; Jack O'Brien; Jennifer Li; M. S. Krafczyk; Ved G. Shah; Amanda R. Wasserman; Daniel W. Apley; Gautham Narayan

astro-ph.IMMar 4, 2026

SELDON: Supernova Explosions Learned by Deep ODE Networks

Authors: Jiezhong Wu, Jack O'Brien, Jennifer Li, M. S. Krafczyk, Ved G. Shah, Amanda R. Wasserman, Daniel W. Apley, Gautham Narayan, +1 more

Organizations: NSF-Simons AI Institute for the Sky (SkAI), Chicago, IL, USA · Department of Industrial Engineering and Management Sciences, Northwestern University · Department of Astronomy, University of Illinois Urbana-Champaign · National Center for Supercomputing Applications (NCSA), Urbana, IL, USA · Department of Physics and Astronomy, Northwestern University · Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University · Department of Statistics and Data Science, Northwestern University

Abstract

The discovery rate of optical transients will explode to 10 million public alerts per night once the Vera C. Rubin Observatory's Legacy Survey of Space and Time comes online, overwhelming the traditional physics-based inference pipelines. A continuous-time forecasting AI model is of interest because it can deliver millisecond-scale inference for thousands of objects per day, whereas legacy MCMC codes need hours per object. In this paper, we propose SELDON, a new continuous-time variational autoencoder for panels of sparse and irregularly time-sampled (gappy) astrophysical light curves that are nonstationary, heteroscedastic, and inherently dependent. SELDON combines a masked GRU-ODE encoder with a latent neural ODE propagator and an interpretable Gaussian-basis decoder. The encoder learns to summarize panels of imbalanced and correlated data even when only a handful of points are observed. The neural ODE then integrates this hidden state forward in continuous time, extrapolating to future unseen epochs. This extrapolated time series is further encoded by deep sets to a latent distribution that is decoded to a weighted sum of Gaussian basis functions, the parameters of which are physically meaningful. Such parameters (e.g., rise time, decay rate, peak flux) directly drive downstream prioritization of spectroscopic follow-up for astrophysical surveys. Beyond astronomy, the architecture of SELDON offers a generic recipe for interpretable and continuous-time sequence modeling in any time domain where data are multivariate, sparse, heteroscedastic, and irregularly spaced.

Figures & tables

Figure 1: Architecture of our proposed SELDON, a customized VAE with band-aware GRU-ODE encoder and interpretable Gaussian-basis decoder. A light curve described by a series of flux observations in various filter bands is encoded to an initial hidden state with the GRU-ODE. The hidden state is evolved with the neural ODE forward in time to form a trajectory on a regularly-sampled grid. This trajectory is then interpreted by a Deep Sets layer to an approximate posterior latent vector. The latent vector is then decoded into a series of basis function parameters representing the history and future evolution of the light curve at all times in all filter bands.

Figure 2: An illustration of a light curve observed over time across six bands indicated in distinct colors, where the total number of observations is in the $99^{\text{th}}$ percentile of all light curves. The error bars for each observation represent the observed flux errors.

Panel of Figure 3 — Figure 3: Out-of-sample forecasting performance as a function of the fraction of the light curve that has been observed. Left : mean absolute $Z$ -score ( $\mathrm{mean}\,|Z|$ ). Center : worst-case absolute $Z$ -score ( $\mathrm{max}\,|Z|$ , log-scale). Right : normalised RMSE. Lower is better in all panels. SELDON (i.e., GRU-ODE) (green) consistently produces the lowest tail and aggregate errors. A plain masked-GRU (orange) has the best median at $10\%$ observed but is outperformed by SELDON afterward. Deep Sets (blue) shows competitive medians, yet the heaviest tails.

Model	Masked-GRU	Deep Sets	SELDON
hidden_dim	256	256	128
Learning Rate	0.0001	0.002	0.002
Batch Size	2048	2048	2048

Table 1: Hyperparameters for the three encoder models compared within this work. Hyperparameters were optimized through grid search.

	Mean $\|Z\|$ $\ \downarrow$			Max $\|Z\|$ $\ \downarrow$			NRMSE $\ \downarrow$
Fraction	Deep Sets	Masked-GRU	SELDON	Deep Sets	Masked-GRU	SELDON	Deep Sets	Masked-GRU	SELDON
0.1	11.885	10.315	10.513	848.772	168.496	159.292	0.076	0.066	0.052
0.2	9.862	10.237	8.929	309.186	164.536	151.551	0.065	0.067	0.045
0.3	7.966	10.031	7.089	224.164	156.688	144.667	0.058	0.072	0.049
0.4	6.525	9.792	5.673	220.531	149.150	115.359	0.051	0.072	0.041
0.5	5.193	9.526	4.295	185.677	147.793	104.237	0.044	0.073	0.034

Table 2: Out–of–sample performance per fraction of observed values. Down arrows next to the metrics indicate lower values are better. Bold values indicate best overall performance across all models.

Figure 4: Violin plots of the signed standardized residuals for out-of-sample forecasts per fraction observed, in each of the three models. These residuals are clipped between $\pm 5$ for visual clarity.

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Irregular Time-Series Modeling Neural Processes

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Astrophysical observations from Earth are subject to weather, environmental, and scientific constraints that lead to sparse, irregular light curves. On the eve of the Vera C. Rubin Observatory Legacy Survey of Space and Time, its dataset offers unprecedented opportunities for transient science. Yet a key challenge remains its cadence, sparse and irregular across six bands, limiting inference. Interpolation helps mitigate this, with Gaussian Processes the standard, but they struggle with cross-band correlations, require a priori kernel specification, and must be fit to each light curve individually, hence scaling poorly. Here, we introduce the neural process family for light curve reconstruction, combining the probabilistic framework of Gaussian Processes with the scalability of deep learning. By meta-learning on diverse simulated transients, Attentive Neural Processes shift the bulk of computation to training, enabling rapid, amortized inference with a class-agnostic model. Evaluated on realistic Rubin cadences across 15 transient classes, we show that even an unoptimized, out-of-the-box Attentive Neural Process consistently outperforms all benchmarks -- a suite of Gaussian Processes and neural networks -- on every tested metric, spanning regression quality, astrophysical feature recovery, and probabilistic calibration. Our model interpolates all bands simultaneously in microseconds, over four orders of magnitude faster than the next-best neural benchmark and five faster than Gaussian Processes, demonstrating the potential of neural processes for the nightly Rubin alert stream. Attentive Neural Processes avoid the overconfidence of standard neural networks and the underconfidence of Gaussian Processes, delivering sharp, well-calibrated uncertainties. This work establishes the neural process family as a scalable, probabilistic foundation for real-time transient science in the Rubin era.

Abstract

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