Related papers: Analysis of fluid flow models
The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…
Turbulent flows are chaotic and unsteady, but their statistical distribution converges to a statistical steady state. Engineering quantities of interest typically take the form of time-average statistics such as $ \frac{1}{t} \int_0^t f (…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established.…
Big data and machine learning are driving comprehensive economic and social transformations and are rapidly re-shaping the toolbox and the methodologies of applied scientists. Machine learning tools are designed to learn functions from data…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
Markov Chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary…
We consider sequences $(X_t^N)_{t\geq0}$ of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form $\dot{x}_t=b(x_t)$, where $b(x)={\pmatrix{-\mu 0 0 \lambda}}x+\tau(x)$…
This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service…
Multi-scale, multi-fidelity numerical simulations form the pillar of scientific applications related to numerically modeling fluids. However, simulating the fluid behavior characterized by the non-linear Navier Stokes equations are often…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals,…
The fluid dynamics community has increasingly adopted machine learning to analyze, model, predict, and control a wide range of flows. These methods offer powerful computational capabilities for regression, compression, and optimization. In…
Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple…