AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
TL;DR
This work introduces Schur–Riesz refinement, a variational framework for combining ordinary polynomial finite-element refinement with functions derived from known PDE structure, thereby bridging width-optimal spaces and stable, computable adaptive approximation.
Width theory identifies economical spaces for compact PDE solution families, but does not provide a stable adaptive selection rule. We introduce Schur-Riesz refinement, which compares ordinary h/p refinement with operator-informed functions on a common variational scale. Projection removes content already represented b...
We introduce two derivative-free spectral projection methods for large-scale monotone equations with convex constraints. The first, SOPP (Spectral Optimal-Perry Projection), selects its Perry parameter by minimizing the condition number of a symmetrized Perry matrix over its positive definite range, in place of the eig...
We establish whole-sequence convergence of the primal iterates of the smoothing-based full-splitting proximal subgradient method (S-FSPS) of Bo\c{t}, Li, and Tao (SIAM J. Optim., 35 (2025), pp.~2623--2653) with a prescribed, nonsummable sequence of vanishing smoothing parameters. The challenge is that each iteration us...
Nonlinear-manifold reduced-order models for parametrized finite element problems can achieve substantial compression both in the number of generalized (latent) coordinates and, through sampling-and-weighting hyperreduction, in the number of sampled elements/integration points. Yet current sampling-and-weighting approac...
We study optimal sampling recovery in reproducing kernel Hilbert spaces (RKHS) in the uniform norm. For every RKHS with bounded kernel, we establish new comparisons between linear sampling widths and Gelfand widths that overcome the known square-root gap, without requiring a measure or a Christoffel-type condition. Our...
Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values. Under scattered or adaptive refinement, the resulting conditioning sigma-algebras need not be nested, so martingale convergence does not justify the sensor limit. We prove strong $L^2$ conver...
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