Physics-Informed Neural Networks for Bose-Einstein Condensates: Continuous Regularisation and Benchmarking in Double-Well Potentials

We assess whether Physics-Informed Neural Networks (PINNs) can capture spontaneous symmetry breaking (SSB) in the stationary Gross–Pitaevskii equation for double-well potentials. For attractive interactions (g < 0), the PINN successfully captures the qualitative features of macroscopic quantum self-trapping, yielding a robust asymmetric population imbalance (|Z| ~ 0.99). For repulsive interactions (g > 0), the unregularised network converges to spurious asymmetric solutions, but a continuous parity regularisation term effectively restores the symmetric ground state (|Z| ≲ 10.2). Benchmarking against a spectral imaginary-time reference, the post-hoc chemical potential agrees to within 2.3% across the full interaction range and to better than 0.6% for g ≥ −1, with density errors of order 10 −2 –10 −3 . We reproduce the two-mode model parameters (2K, B, Δγ) using full GPE eigenstates and show that the asymmetric branch of the two-mode model, although formally present (Λ ≫ 2), corresponds to higher-energy self-trapped states for repulsive interactions, explaining why the ground state remains symmetric for g > 0.