T S B Sudarshan

Giacomo Dimarco, Axel Klar, Theresa Köfler et al.

This work introduces a novel high-order numerical framework for solving kinetic equations, designed to remain uniformly valid across all regimes of the mean free path, spanning from the rarefied kinetic scale to the incompressible hydrodynamic limit. The method is built upon a micro-macro decomposition, which reformulates the underlying kinetic equation into a coupled system consisting of a macroscopic part, representing the fluid-dynamic evolution, and a microscopic part, describing the non-equilibrium deviations. The proposed framework ensures high-order temporal accuracy through the use of Implicit-Explicit Runge-Kutta methods, which provide stability and efficiency in stiff regimes, while spatial resolution is enhanced by combining finite-difference WENO reconstructions with high-order central difference approximations. A key feature of the proposed methodology is its Asymptotic-Preserving (AP) property. We demonstrate that, in the appropriate asymptotic limit as the mean free path tends to zero, the scheme consistently reduces to a high-order finite-difference formulation of the incompressible Navier-Stokes equations. To support the theoretical findings, a set of numerical experiments are performed on one- and two-dimensional benchmark problems, which confirm the accuracy, stability, and versatility of the method across different flow regimes.

Chethana Prasad Kabgere, Sudarshan T S B

Advanced Driver Assistance Systems (ADAS) increasingly employ Federated Learning (FL) to collaboratively train models across distributed vehicular nodes while preserving data privacy. Yet, conventional FL aggregation remains susceptible to noise, latency, and security constraints inherent to real-time vehicular networks. This paper introduces Noise-Resilient Quantum Federated Learning (NR-QFL), a hybrid quantum-classical framework that enables secure, low-latency aggregation through variational quantum circuits (VQCs) operating under Noisy Intermediate-Scale Quantum (NISQ) conditions. The framework encodes model parameters as quantum states with adaptive gate reparameterization, ensuring bounded-error convergence and provable resilience under Completely Positive Trace-Preserving (CPTP) dynamics. NR-QFL employs quantum entropy-based client selection and multi-server coordination for fairness and stability. Empirical validation shows consistent convergence with reduced gradient variance, lower communication overhead, and enhanced noise tolerance under constrained edge conditions. The framework establishes a scalable foundation for quantum-enhanced federated learning, enabling secure, efficient, and dynamically stable ADAS intelligence at the vehicular edge.