FOSLS-deRhaNN: native de Rham neural classes for H(div) and H(curl) with applications to first-order system least-squares neural network methods for partial differential equations

Excerpt

arXiv:2610.08016v1 Announce Type: cross Abstract: We construct neural approximation classes native to the graph spaces H(div) and H(curl), in two and three dimensions and, for H(div), in any dimension. Every realization lies in the space for all parameter values, and with kinked potentials, such as ReLU networks, the admissible jumps appear at finite width. The classes are images of scalar and componentwise networks under fixed operators of the de Rham complex, and do not involve a mesh or finit