MANGO:Multi-Angle Neural Gated Operators for Chirp-Perturbed PDEs

We introduce **MANGO** (Multi-Angle Neural Gated Operator), a spectral neural operator for chirp-perturbed PDEs whose solutions exhibit a local spectral content that rotates continuously with position. MANGO maintains multiple fractional Fourier transform (FRFT) branches whose angles are learnable parameters, optimized jointly with the spectral weights and a position-dependent softmax gate that combines branches at every spatial location. The architecture is matched to the structure of the problem class: the FRFT at angle $\alpha_0$ diagonalizes the chirp-perturbed PDE whose intrinsic angle is $\alpha_0$, and MANGO's learnable angles let the architecture discover $\alpha_0$ from data when it is unknown or varies across the domain—neither of which classical FRFT methods accommodate. We further introduce a Mihlin–Hörmander regularizer on the spectral weights of each non-Fourier branch, encouraging each branch to act as a bounded operator on $L^p$ for $1 < p < \infty$. We construct four chirp-perturbed PDE benchmarks with closed-form ground truth, positioned as identifiability tests. On these benchmarks, MANGO recovers the intrinsic spectral structure of each PDE from supervised solution data alone and achieves state-of-the-art performance against six neural-operator baselines.