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

TL;DR

This paper presents a physics-informed neural network approach to accurately reconstruct electric fields in noble-element TPCs, reducing calibration data needs and improving position accuracy for rare-event detection.

Contribution

We develop a continuous normalizing flow model that enforces physical constraints, improving electric field learning from calibration data over traditional methods.

Findings

Achieves better reconstruction accuracy than histogram-based methods.

Reduces calibration data requirements by an order of magnitude.

Enables practical field monitoring and improved background discrimination.

Abstract

Accurate position reconstruction in noble-element time-projection chambers (TPCs) 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 $\mathcal{O}(10^7)$ 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 $^{83\mathrm{m}}$Kr calibration data in an XLZD-like dual-phase xenon TPC, our method achieves superior reconstruction accuracy compared to histogram-based corrections when trained on identical datasets, demonstrating viable performance with only $6\times10^5$ events$\unicode{x2013}$an order of magnitude reduction in calibration requirements. This approach enables practical monthly field monitoring campaigns, propagation of position uncertainties through differentiable transformations, and enhanced background discrimination in next-generation rare-event searches.