5 papers · 1 filter
Advancements in Fractional Neural Operators with Adaptive Hybrid Kernels in Multiscale Sobolev Spaces
Romulo Damaselin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper introduces significant advancements in fractional neural operators (FNOs) through the integration of adaptive hybrid kernels and stochastic multiscale analysis. We addre…
Non-Linear Interactions in Neural Network Operators: New Theorems on Symmetry-Preserving Transformations
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose…
Voronovskaya-Type Asymptotic Expansions and Convergence Analysis for Neural Network Operators in Complex Domains
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper extends the classical theory of Voronovskaya-type asymptotic expansions to generalized neural network operators defined on non-Euclidean and fractal domains. We introduc…
Generalized Lagrangian Coherent Structures in Finsler Manifolds
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler m…
Semiclassical and Microlocal Analysis of Energy Dissipation and Cascades in Turbulent Flows
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This work presents a comprehensive study of the microlocal energy decomposition and propagation of singularities for semiclassically adjusted dissipative pseudodifferential operato…