Math: Pde

Machine-learning ideas tagged Pde in the Math taxonomy of the Math2NN corpus.

Unverified 2026

Anisotropic Anharmonic Diffusion Layer

Insert a learnable semigroup layer that evolves features according to a positive operator combining frequency damping and spatially varying confinement. Unlike isotropic Gaussian smoothing, the layer can damp selected frequencies differently along different axes and can suppress activations in learned spatial regions, while the positive-semigroup construction prevents amplification.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Sharp Time-Decay Estimates for Fractional Heat Semigroups Associated with Polynomial Anharmonic Oscillators arXiv:2607.17580