Degeneracy-Aware Pulsar Parameter Estimation from Light Curves via Deep Learning and Test-Time Optimization

TL;DR

This work tackles the problem of degeneracies in pulsar parameter estimation from light curves, which render single-point DL predictions insufficient and make MCMC impractically slow. It introduces a Transformer-LSTM architecture that predicts a Gaussian Mixture Model with $K=10$ components to represent multiple high-likelihood parameter sets, augmented by a forward-model emulator-based loss and a dissimilarity term to promote diverse solutions, plus a test-time optimization step to refine predictions for each observed light curve. On simulated data and NICER observations of PSR J0030+0451, the method achieves light curves that closely match observations and performs comparably to MCMC methods while reducing inference time to about 4 minutes per case, thereby enabling scalable, degenerate-aware pulsar parameter estimation. While it does not provide the full posterior distribution, this approach identifies high-likelihood regions efficiently and offers practical, real-time inference for multi-messenger astronomy, with future work aimed at expanding the GMM capacity and exploring broader parameter spaces.

Abstract

Probing properties of neutron stars from photometric observations of these objects helps us answer crucial questions at the forefront of multi-messenger astronomy, such as, what is behavior of highest density matter in extreme environments and what is the procedure of generation and evolution of magnetic fields in these astrophysical environments? However, uncertainties and degeneracies-where different parameter sets produce similar light curves-make this task challenging. We propose a deep learning framework for inferring pulsar parameters from observed light curves. Traditional deep learning models are not designed to produce multiple degenerate solutions for a given input. To address this, we introduce a custom loss function that incorporates a light curve emulator as a forward model, along with a dissimilarity loss that encourages the model to capture diverse, degenerate parameter sets for a given light curve. We further introduce a test-time optimization scheme that refines predicted parameters by minimizing the discrepancy between the observed light curve and those reconstructed by the forward model from predicted parameters during inference. The model is trained using a suite of state-of-the-art simulated pulsar light curves. Finally, we demonstrate that the parameter sets predicted by our approach reproduce light curves that are consistent with the true observation.

Figures (4)

• Figure 1: Simulated thermal light curve from a pulsar.
• Figure 2: Block diagram of the proposed training methodology for pulsar parameter estimation from light curves. A transformer encoder first extracts key features $F_E$ from the input light curve $x$, which are then processed by a LSTM network that sequentially predicts the components of GMM $\{(\mu_1, \sigma_1), (\mu_2, \sigma_2), (\mu_3, \sigma_3), \ldots, (\mu_k, \sigma_k)\}$. To encourage diversity among the GMM components, a dissimilarity loss is employed. Each component $\theta_k=\mu_k, \sigma_k$ is passed through a forward model $f$ to generate corresponding light curve $\hat{\mathbf{x}}_k = f(\mu_k, \sigma_k)$. The negative log-likelihood (NLL) between the generated light curves and the input light curve is then computed to to guide the model toward better parameter estimation.
• Figure 3: Comparison of predicted vs. true light curves for NICER's PSR J0030+0451 observation. The red curve is the real observation. The grey curves correspond to our predicted pulsar parameters upon analysis of this pulsar event. The green and blue curves correspond to most likely parameters produced by the traditional MCMC and MCMC with nested sampling methods respectively. The left and right panels show predictions from this work without and with test-time optimization respectively. As can be seen, the test-time optimized predictions show strong alignment with the observation, and are comparable to those obtained using MCMC and MCMC with nested sampling.
• Figure 4: Comparison of predicted vs. true light curves for the testing data. The red curve represents the true light curve, while the grey curves show the predicted light curves based on our analysis of the pulsar event. The left and right panels illustrate the best-case and worst-case prediction scenarios, respectively, within the testing dataset.