Related papers: Reservoir computing model of two-dimensional turbu…
By utilizing diffusion maps embedding and transition matrix analysis we investigate sparse temperature measurement time-series data from Rayleigh--B\'enard convection experiments in a cylindrical container of aspect ratio $\Gamma=D/L=0.5$…
The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number…
A weighted residual collocation methodology for simulating two-dimensional shear-driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
Despite the significant breakthrough of neural networks in the last few years, their spreading in the field of computational fluid dynamics is very recent, and many applications remain to explore. In this paper, we explore the drag…
A model for three-dimensional Rayleigh-B\'{e}nard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic…
Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-B\'{e}nard convection and Taylor-Couette flow display self-organized large-scale flow patterns. How do small-scale turbulent fluctuations impact the…
Direct numerical simulations (DNS) indicate that at large values of the Rayleigh number ($Ra$) convection in porous media self-organizes into narrowly-spaced columnar flows, with more complex spatiotemporal features being confined to…
We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations,…
Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic…
Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the $2^\text{nd}$ order Runge-Kutta. It…
The stratified inclined duct (SID) flow provides a canonical model for sustained, buoyancy-driven exchange between two reservoirs of different density, and emerges as a new paradigm in geophysical fluid dynamics. Yet, the flow dynamics…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
We present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh-B\'{e}nard (RB) convection over the Rayleigh number range $10^8 \leqslant Ra\leqslant 10^{10}$ and the Prandtl number range…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them…
Reservoir computing derived from recurrent neural networks is more applicable to real world systems than deep learning because of its low computational cost and potential for physical implementation. Specifically, physical reservoir…
Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or \emph{reservoir}, to approximate and predict time series data. The scale, speed and power usage of reservoir computers could be enhanced by…
Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…