22 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…
Generalized Neural Network Operators with Symmetrized Activations: Fractional Convergence and the Voronovskaya-Damasclin Theorem
Rômulo Damasclin Chaves dos Santos
This paper explores the asymptotic behavior of univariate neural network operators, with an emphasis on both classical and fractional differentiation over infinite domains. The ana…
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…
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…
Mathematical Analysis of Regularity, Bifurcations, and Turbulence in Fluid Dynamics via Sobolev, Besov, and Triebel-Lizorkin Spaces
Rômulo Damasclin Chaves dos Santos
This article presents a comprehensive mathematical framework for the study of regularity, bifurcations, and turbulence in fluid dynamics, leveraging the power of Sobolev and Besov…
Quantum-Inspired Stochastic Modeling and Regularity Analysis in Turbulent Flows
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integ…
Dissipation and Regularity in the Smagorinsky Model with Dynamic Boundaries
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This article presents an innovative extension of the Smagorinsky model incorporating dynamic boundary conditions and advanced regularity methods. We formulate the modified Navier-S…
Adaptive Dissipation in the Smagorinsky Model for Turbulence in Boundary-Driven Flows
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper enhances the classic Smagorinsky model by introducing an innovative, adaptive dissipation term that adjusts dynamically with distance from boundary regions. This modific…
A High-Order Analytical Extension of the Corrected Smagorinsky Model for Non-Equilibrium Turbulent Flow
Rômulo Damasclin Chaves dos Santos
This study presents an extension of the corrected Smagorinsky model, incorporating advanced techniques for error estimation and regularity analysis of far-from-equilibrium turbulen…
Advanced Theoretical Analysis of Stability and Convergence in Computational Fluid Dynamics for Computer Graphics
Rômulo Damasclin Chaves dos Santos
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This…
Enhanced Diffusion in Anisotropic and Non-uniform Geometries
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
Enhanced diffusion, which describes the accelerated spread of passive scalars due to the interaction between advection and molecular diffusion, has been extensively studied in simp…
Stochastic Trajectories and Spectral Boundary Conditions for Enhanced Diffusion in Immersed Boundary Problems
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic traject…
Hybrid Adaptive Dual Reciprocity Method for Efficient Solution of Large-Scale Non-Linear Boundary Conditions
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems,…
Vortex Formation and Dissipation in Chaotic Flows: A Hypercomplex Approach
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riem…
High-Order Dynamic Integration Method (HODIM) for Modeling Turbulent Fluid Dynamics
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent f…
Quantum-Inspired Stochastic Modeling and Regularity in Turbulent Fluid Dynamics
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales, Erickson F. M. S. Silva
This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with frac…
Hypercomplex Dynamics and Turbulent Flows in Sobolev and Besov Functional Spaces
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales
This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity…