HEAL-PINN: Physics-Informed Swin Transformer for Dark Matter Studies for Sparse Lensing Data

Strong gravitational lensing offers a powerful probe of the nature of dark matter from the morphology of its substructure. While expected to change in the next few years, current available data is sparse, making analyses of lensing systems for extraction of dark-matter properties difficult. In this work we propose a physics-informed Swin Transformer model, including a novel HEAL-Swin variant with the gravitational lensing equation embedded in the architecture, to classify between different models for dark matter from simulated lensing systems. We test the classification performance of various Swin Transformer models on a small dataset of these simulated lensing images, mimicking the current availability of lenses. The architectures include a base Swin Transformer model, a Swin Transformer model with the lensing equation baked into its architecture, a HEAL-Swin model, and HEAL-Swin with a physics-informed architecture. We then evaluate the models based on the evolution of Receiver Operating Characteristic Area Under the Curve (ROC AUC) and demonstrate that physics-informed HEAL-Swin evolves ROC AUC the fastest among all tested models.