Physics-Calibrated Image-Space Inference for Strong Gravitational Lensing

Strong gravitational lensing provides critical insights into cosmology, but upcoming Stage-IV surveys will discover hundreds of thousands of lenses, rendering traditional Markov Chain Monte Carlo inference computationally intractable. While machine learning offers millions-fold speedups, standard data-driven models operate as black boxes that ignore the laws of physics, leading to brittle and uncalibrated results on real observational data. In this work, we introduce a Physics-Informed Neural Network (PINN) framework for gravitational lens mass reconstruction. By embedding the governing equations of general relativity, specifically the two-dimensional Poisson equation, directly into the neural latent space, our approach bridges the gap between high-speed inference and exact physical compliance. We present a comprehensive empirical study demonstrating that this physics-calibrated architecture achieves statistically significant improvements in accuracy and uncertainty calibration compared to traditional and unconstrained neural baselines. Furthermore, we demonstrate the framework’s robustness on real Hubble Space Telescope observations and extend its capabilities to multi-messenger astronomy by integrating stellar kinematics and gravitational wave diffraction spectra.