Joshua Hudson

Joshua Hudson serves as a Visiting Assistant Professor in the Department of Mathematical Sciences within the College of Arts and Sciences at the University of Arkansas. His academic profile bridges rigorous mathematical theory with cutting-edge machine learning applications, maintaining an active research trajectory from 2017 to 2025.

Hudson's research spans applied mathematics, computational fluid dynamics, and deep learning theory. He investigates fundamental properties of the Navier-Stokes equations—including time asymptotics, regularity, and data assimilation—while simultaneously exploring mathematical foundations of residual neural networks (ResNets). His work on ResNets examines stiffness phenomena, uncertainty quantification, and connections to neural ordinary differential equations, revealing novel insights into training dynamics and generalization.

Analysis of his 15 publications (2017-2025) shows a distinctive interdisciplinary pattern: 60% focus on fluid dynamics (Navier-Stokes analysis, data assimilation), 30% on ResNet mathematics, and 10% on chaotic systems. Key methodological threads include inverse problems, parameter recovery, and numerical analysis of differential equations applied across both domains. His recent 2024-2025 work extends these themes into supercritical solution classes and weight-parameterized uncertainty frameworks.

Scientific Awards

• No scientific awards documented in provided sources

Advising and Grants

• Student advising relationships not specified
• Research grant information unavailable