Physics Informed Neural Network (PINN) and Spherical Harmonic–PINN Approaches for B0 field reconstruction in the LANL nEDM Experiment

The Los Alamos National Laboratory neutron electric dipole moment experiment (LANL nEDM) targets a statistical sensitivity of 2 ×10−27 e·cm using Ramsey's method of separated oscillatory fields for ultracold neutrons stored in a double precession chamber geometry. To mitigate systematic effects associated with magnetic field non-uniformities, the experiment requires a highly uniform magnetic field in the precession chamber region, with gradients suppressed to < 0.1 nT/m. We present a novel concept based on a Physics-Informed Neural Network (PINN) and spherical harmonic expansion to model the magnetic field produced by the B0 coil. In the PINN approach, the network minimizes a composite loss function combining the mean-squared error (MSE) between predicted and measured values with the divergence-free (∇·B = 0) and curl-free (∇×B = 0) constraints. In the hybrid approach, the measured field is first represented by a spherical harmonic expansion truncated at some degree ℓmax, and the residual field is then reconstructed using a PINN. By enforcing∇·B = 0 and ∇×B = 0, both approaches reconstruct a well-characterized three-dimensional magnetic field within the precession region generated by the B0 coil.