Examination of optimizing information flow in networks

The central role of the Internet and the World-Wide-Web in global communications has refocused much attention on problems involving optimizing information flow through networks. The most basic formulation of the question is called the "max flow" optimization problem: given a set of channels with prescribed capacities that connect a set of nodes in a network, how should the materials or information be distributed among the various routes to maximize the total flow rate from the source to the destination. Theory in linear programming has been well developed to solve the classic max flow problem. Modern contexts have demanded the examination of more complicated variations of the max flow problem to take new factors or constraints into consideration; these changes lead to more difficult problems where linear programming is insufficient. In the workshop we examined models for information flow on networks that considered trade-offs between the overall network utility (or flow rate) and path diversity to ensure balanced usage of all parts of the network (and to ensure stability and robustness against local disruptions in parts of the network). While the linear programming solution of the basic max flow problem cannot handle the current problem, the approaches primal/dual formulation for describing the constrained optimization problem can be applied to the current generation of problems, called network utility maximization (NUM) problems. In particular, primal/dual formulations have been used extensively in studies of such networks. A key feature of the traffic-routing model we are considering is its formulation as an economic system, governed by principles of supply and demand. Considering channel capacities as a commodity of limited supply, we might suspect that a system that regulates traffic via a pricing scheme would assign prices to channels in a manner inversely proportional to their respective capacities. Once an appropriate network optimization problem has been formulated, it remains to solve the optimization problem; this will need to be done numerically, but the process can greatly benefit from simplifications and reductions that follow from analysis of the problem. Ideally the form of the numerical solution scheme can give insight on the design of a distributed algorithm for a Transmission Control Protocol (TCP) that can be directly implemented on the network. At the workshop we considered the optimization problems for two small prototype network topologies: the two-link network and the diamond network. These examples are small enough to be tractable during the workshop, but retain some of the key features relevant to larger networks (competing routes with different capacities from the source to the destination, and routes with overlapping channels, respectively). We have studied a gradient descent method for solving obtaining the optimal solution via the dual problem. The numerical method was implemented in MATLAB and further analysis of the dual problem and properties of the gradient method were carried out. Another thrust of the group's work was in direct simulations of information flow in these small networks via Monte Carlo simulations as a means of directly testing the efficiencies of various allocation strategies

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

Integrated design and control of chemical processes : part I : revision and clasification

[EN] This work presents a comprehensive classification of the different methods and procedures for integrated synthesis, design and control of chemical processes, based on a wide revision of recent literature. This classification fundamentally differentiates between “projecting methods”, where controllability is monitored during the process design to predict the trade-offs between design and control, and the “integrated-optimization methods” which solve the process design and the control-systems design at once within an optimization framework. The latter are revised categorizing them according to the methods to evaluate controllability and other related properties, the scope of the design problem, the treatment of uncertainties and perturbations, and finally, the type the optimization problem formulation and the methods for its resolution.[ES] Este trabajo presenta una clasificación integral de los diferentes métodos y procedimientos para la síntesis integrada, diseño y control de procesos químicos. Esta clasificación distingue fundamentalmente entre los "métodos de proyección", donde se controla la controlabilidad durante el diseño del proceso para predecir los compromisos entre diseño y control, y los "métodos de optimización integrada" que resuelven el diseño del proceso y el diseño de los sistemas de control a la vez dentro de un marco de optimización. Estos últimos se revisan clasificándolos según los métodos para evaluar la controlabilidad y otras propiedades relacionadas, el alcance del problema de diseño, el tratamiento de las incertidumbres y las perturbaciones y, finalmente, el tipo de la formulación del problema de optimización y los métodos para su resolución