Title: PHYSICS-INFORMED RADIAL PHASE RETRIEVAL NEURAL NETWORK WITH HYBRID DEEP PRIORS AND DUAL PDE
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: phase retrieval;PDE networks; outer-ring extrapolation; inverse problems

Abstract: Phase retrieval from intensity-only measurements is severely ill-posed due to global-gauge and rotational symmetries. We consider outer-ring generalization: training with supervision from only a few inner rings and testing the model’s ability to reconstruct a broader set of unseen outer rings. We introduce a physics-informed hybrid network that combines (i) radial priors encoded by a smooth exponentiated spline and a \emph{monotone} outer-radius booster, (ii) two differentiable PDE branches---a Strang-split Kerr--NLSE pathway for high-frequency synthesis and a TIE-based low-pass pathway for coarse structure---and (iii) a strict radial projection enforcing output symmetry, together with a radius-dependent $\alpha$-fusion. Across the tested configurations, when trained only on a few rings (1-3), our model reconstructs more rings(4-9) than conventional methods, and achieves better stability in peak
positions and amplitude calibration under out-of-distribution settings. This provides some inspiration for enhancing the generalization of physics-informed neural networks when applied to optical inverse problems. Ablations isolate the contribution of the alpha fusion, PDE coupling, and monotone
boosting. We will release pseudo-code to facilitate reproducibility.

TL;DR: a pde based physic informed neural network that performs well in generalization