Related papers: Ergodic optimization in dynamical systems
In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a $C^2$ flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space $\mc…
Aerodynamic optimization is ubiquitous in the design of most engineering systems interacting with fluids. A common approach is to optimize a performance function defined by a choice of an aerodynamic model, e.g., turbulence RANS model, and…
The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits well-defined projections onto the…
This paper develops KL-Ergodic Exploration from Equilibrium ($\text{KL-E}^3$), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables…
Thermodynamics of small systems has become an important field of statistical physics. They are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
Consider a homeomorphism $f$ defined on a compact metric space $X$ and a continuous map $\phi\colon X \to \mathbb{R}$. We provide an abstract criterion, called \emph{control at any scale with a long sparse tail} for a point $x\in X$ and the…
Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The…
Autonomous robotic exploration in remote and extreme environments allows scientists to model complex transport phenomena and collective behaviors described by continuously deforming flow fields. Although these environments are naturally…
We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
The explicit expression of ergotropy (a.k.a. available energy) of a classical system is known for the case when the system phase space density is continuous and with no plateaus. Here we provide the general expression of ergotropy that…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…
Obtaining sharp estimates for quantities involved in a given model is an integral part of the modeling process. For dynamical systems whose orbits display a complicated, perhaps chaotic, behaviour, the aim is usually to estimate time or…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Consider a transitive expanding dynamical system $ \sigma: \Sigma \to \Sigma $, and a H\"older potential $ A $. In ergodic optimization, one is interested in properties of $A$-maximizing probabilities. Assuming ergodicity, it is already…
Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a…
We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of…
The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same…