18 papers
Stochastic Fractional Neural Operators: A Symmetrized Approach to Modeling Turbulence in Complex Fluid Dynamics
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a…
Revolutionizing Fractional Calculus with Neural Networks: Voronovskaya-Damasclin Theory for Next-Generation AI Systems
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This work introduces rigorous convergence rates for neural network operators activated by symmetrized and perturbed hyperbolic tangent functions, utilizing novel Voronovskaya-Damas…
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…
Extension of Symmetrized Neural Network Operators with Fractional and Mixed Activation Functions
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing mo…
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…