Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation
The study develops a new space-time Barron framework to approximate solutions of fractional parabolic partial differential equations, capturing their anisotropic structure. This leads to a dimension-efficient approximation bound in mixed Sobolev norms, showing neural networks can efficiently model these solutions by leveraging the intrinsic regularity of the solution spaces.