[Paper Review] Inferring astrophysical X-ray polarization with deep learning

Nikita Moriakov, Ashwin Samudre+4 more|arXiv (Cornell University)|May 16, 2020

Particle Detector Development and Performance14 references4 citations

TL;DR

This paper proposes deep learning models—specifically a VGG-16 ensemble for polarization angle estimation and a fine-tuned ResNet-34 for impact point localization—to improve X-ray track reconstruction from IXPE data. The models achieve reconstruction efficiency comparable to the state-of-the-art analytical method, with the added benefit of uncertainty estimation and potential for future performance gains through architectural and preprocessing refinements.

ABSTRACT

We investigate the use of deep learning in the context of X-ray polarization detection from astrophysical sources as will be observed by the Imaging X-ray Polarimetry Explorer (IXPE), a future NASA selected space-based mission expected to be operative in 2021. In particular, we propose two models that can be used to estimate the impact point as well as the polarization direction of the incoming radiation. The results obtained show that data-driven approaches depict a promising alternative to the existing analytical approaches. We also discuss problems and challenges to be addressed in the near future.

Motivation & Objective

• Address the limitations of current analytical methods in reconstructing X-ray photon tracks from IXPE data, particularly their poor performance on low-energy events.
• Develop data-driven deep learning approaches to estimate the impact point and polarization direction of X-ray photons with higher accuracy than existing methods.
• Explore the feasibility of using neural networks to improve reconstruction efficiency and enable uncertainty quantification in astrophysical X-ray polarization measurements.
• Identify key challenges in current deep learning implementations for IXPE, including suboptimal preprocessing and non-equivariant convolutions on hexagonal sensor grids.
• Lay the foundation for future improvements through multi-task learning, hexagonal convolutions, and better model calibration.

Proposed method

• Simulated 500,000 photoelectron (PE) track images from an unpolarized X-ray source using Monte Carlo methods, with labels for energy, impact point coordinates, and polarization angle.
• Preprocessed images by normalizing pixel values to [0,1] and upsampling to a square cartesian grid with a factor of ~2 to standardize input dimensions.
• Trained a M-head ensemble of VGG-16 networks for polarization angle estimation using cross-entropy loss and angular regression with periodic boundary conditions.
• Employed transfer learning with a pre-trained ResNet-34 for impact point localization, fine-tuning only the final layer using mean squared error (MSE) loss.
• Used a batch size of 64, initial learning rate of 3e−2, weight decay of 1e−3, and five training epochs, with 20% of training data used for validation.
• Evaluated models on a separate test set of 35,838 observations from a π/4 polarized source at 4 keV, using RMSE for impact point and ε10/modulation factor µ for polarization performance.

Experimental results

Research questions

• RQ1 Can deep learning models outperform or match the reconstruction efficiency of the current analytical method in estimating X-ray photon impact points and polarization angles?
• RQ2 To what extent do data-driven approaches improve the reconstruction of low-energy events, which are poorly handled by analytical methods?
• RQ3 How does the inclusion of uncertainty estimation in deep learning models enhance the reliability and quality control of reconstructed X-ray polarization data?
• RQ4 What are the key limitations of current deep learning implementations for IXPE, particularly regarding image preprocessing and convolutional architecture choice?
• RQ5 Can multi-task learning frameworks that jointly predict impact point and polarization direction improve overall performance compared to single-task models?

Key findings

• The deep learning models achieved reconstruction efficiency (ε10) comparable to the state-of-the-art analytical method, with both methods showing similar performance in capturing the cos² modulation of polarization angles.
• The impact point localization model achieved an RMSE of 7.807 in the x-direction and 7.368 in the y-direction on the test set, indicating accurate spatial reconstruction.
• The polarization angle estimation model demonstrated a modulation factor µ close to that of the analytical method, confirming its ability to reproduce the expected polarization signature.
• The study revealed that current image preprocessing—particularly 2× upsampling from hexagonal to cartesian grids—distorts track aspect ratios and may degrade performance.
• The authors identified that conventional convolutions on hexagonal sensor data are not equivariant, suggesting that hexagonal or group-convolutional networks could yield better results.
• Future improvements such as incorporating impact point coordinates as input features, using hexagonal convolutions, and enhancing model calibration through ensemble methods are expected to further boost performance.