arXiv subjects

Shailendra K. Rathor

Publications and source records attributed to Shailendra K. Rathor.

6 recordsLinked to original sources

arXiv2025

Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different number of degrees of freedom

Reservoir computing (RC) is a powerful framework for predicting nonlinear dynamical systems, yet the role of reservoir topology$-$particularly symmetry in connectivity and weights$-$remains not adequately understood. This work investigates how the structure of the network influences the performance of RC in four systems of increasing complexity: the Mackey-Glass system with delayed-feedback, two low-dimensional thermal convection models, and a three-dimensional shear flow model exhibiting transition to turbulence. Using five reservoir topologies in which connectivity patterns and edge weights are controlled independently, we evaluate both direct- and cross-prediction tasks. The results show that symmetric reservoir networks substantially improve prediction accuracy for the convection-based systems, especially when the input dimension is smaller than the number of degrees of freedom. In contrast, the shear-flow model displays almost no sensitivity to topological symmetry due to its strongly chaotic high-dimensional dynamics. These findings reveal how structural properties of reservoir networks affect their ability to learn complex dynamics and provide guidance for designing more effective RC architectures.

physics.flu-dyn↗

arXiv2024

Asymmetrically connected reservoir networks learn better

We show that connectivity within the high-dimensional recurrent layer of a reservoir network is crucial for its performance. To this end, we systematically investigate the impact of network connectivity on its performance, i.e., we examine the symmetry and structure of the reservoir in relation to its computational power. Reservoirs with random and asymmetric connections are found to perform better for an exemplary Mackey-Glass time series than all structured reservoirs, including biologically inspired connectivities, such as small-world topologies. This result is quantified by the information processing capacity of the different network topologies which becomes highest for asymmetric and randomly connected networks.

cs.NE↗

arXiv2022

Dynamic Scaling in Rotating Turbulence: A Shell Model Study

We investigate the scaling form of appropriate time-scales extracted from time-dependent correlation functions in rotating, turbulent flows. In particular, we obtain precise estimates of the dynamic exponents $z_p$, associated with the time-scales, and their relation with the more commonly measured equal-time exponents $ζ_p$. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

physics.flu-dyn↗

arXiv2022

Predictability in Rotating Turbulence: Insights from a Shell Model Study

We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases with rotation rate to satisfy a power law in Rossby number with a scaling exponent of $-2/3$. Intriguingly, we find that before entering the algebraic growth stage, the error dynamics freezes for a time period determined by the finite Rossby number. We further analyse the scale dependence of the predictability time and observe that it tends to become scale independent in the Zeman range as the Rossby number decreases. Finally, we compute the finite size Lyapunov exponent and validate the dimensional prediction of its scaling $\simδ^{-1}$ for large $δ$ of the order of velocities in the Zeman range for small Rossby numbers.

physics.flu-dyn↗

arXiv2020

Bridging Inertial and Dissipation Range Statistics in Rotating Turbulence

We investigate the connection between the inertial range and the dissipation range statistics of rotating turbulence through detailed simulations of a helical shell model and a multifractal analysis. In particular, by using the latter, we find an explicit relation between the (anomalous) scaling exponents of equal-time structure functions in the inertial range in terms of the generalised dimensions associated with the energy dissipation rate. This theoretical prediction is validated by detailed simulations of a helical shell model for various strengths of rotation from where the statistics of dissipation rate, and thus the generalised dimensions, as well as the inertial range, in particular the anomalous scaling exponents, are extracted. Our work also underlines a surprisingly good agreement---such as in the spatial structure of the energy dissipation rates and the decrease in inertial range intermittency with increasing strengths of rotation---between solutions of the Navier--Stokes equation in a rotating frame with those obtained from low-dimensional, dynamical systems such as the shell model which are not explicitly anisotropic. Finally, we perform direct numerical simulations of the Navier--Stokes equation, with the Coriolis force incorporated, to confirm the robustness of the conclusions drawn from our multifractal and shell model studies.

physics.flu-dyn↗

arXiv2016

Stability Analysis of Convection in the Intracluster Medium

We use the machinery usually employed for studying the onset of Rayleigh--Bénard convection in hydro- and magnetohydro-dynamic settings to address the onset of convection induced by the magnetothermal instability and the heat-flux-buoyancy-driven-instability in the weakly-collisional magnetized plasma permeating the intracluster medium. Since most of the related numerical simulations consider the plasma being bounded between two `plates' on which boundary conditions are specified, our strategy provides a framework that could enable a more direct connection between analytical and numerical studies. We derive the conditions for the onset of these instabilities considering the effects of induced magnetic tension resulting from a finite plasma beta. We provide expressions for the Rayleigh number in terms of the wave vector associated with a given mode, which allow us to characterize the modes that are first to become unstable. For both the heat-flux-buoyancy-driven-instability and the magnetothermal instability, oscillatory marginal stable states are possible.

physics.flu-dyn↗