A new arXiv paper studies fractal interpolation functions built from iterated function systems and combines them with neural network operators. The authors construct alpha-fractal functions and analyze how smoothness is retained alongside convergence guarantees. The work sits at the intersection of approximation theory and neural operator methods.
A new arXiv preprint argues that existing adaptive-mesh methods for neural operators, which solve partial differential equations, focus mostly on deciding where to place sample points. The authors propose an approach that also addresses how the operator should interact with those points, using a gauge-aware transport formulation. The work aims to let operators adapt to local physical features in a more complete way.
The paper studies the approximation and statistical learning of nonlinear functionals defined on reproducing kernel Hilbert spaces (RKHSs) using neural networks. It is motivated by functional data such as time series and images.
A revised arXiv paper investigates how well neural operators, a family of deep learning frameworks for approximating partial differential equation solution operators, handle stiff spatio-temporal dynamics. The work centers on the FitzHugh-Nagumo model, testing translation invariance as a key property for capturing its behavior.