Physics-informed continuous normalizing flows to learn the electric field within a time-projection chamber

Abstract Accurate position reconstruction in noble-element time-projection chambers is critical for rare-event searches in astroparticle physics, yet is systematically limited by electric field distortions arising from charge accumulation on detector surfaces. Conventional data-driven field corrections suffer from three fundamental limitations: discretization artifacts that break smoothness and differentiability, lack of guaranteed consistency with Maxwell’s equations, and statistical requirements of O ( 10 7 ) calibration events. We introduce a physics-informed continuous normalizing flow architecture that learns the electric field transformation directly from calibration data while enforcing the constraint of field conservativity through the model structure itself. Applied to simulated 83 m Kr calibration data in an XLZD-like dual-phase xenon detector, our method achieves superior reconstruction accuracy compared to histogram-based corrections when trained on identical datasets, demonstrating viable performance with approximately 8.9 × 10 4 events—a 50 times reduction in calibration data requirements for a comparable performance to a field distortion correction map generated from approximately 4.5 × 10 6 events. This approach can enable practical monthly field monitoring campaigns, propagation of position uncertainties through differentiable transformations, and enhanced background discrimination in next-generation rare-event searches.