相关论文: On Cucker-Smale dynamical systems with degenerate …

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify…

We study the problem of consensus emergence in multi-agent systems via external feedback controllers. We consider a set of agents interacting with dynamics given by a Cucker-Smale type of model, and study its consensus stabilization by…

We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive…

We study a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, which lends to a similar 1D global well-posedness analysis to…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

This paper is concerned with global existence as well as infinite-time blowups of classical solutions to the following fully parabolic kinetic system \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u) v_t-\Delta v+v=u \end{cases}…

Quantum decoherence is the disappearance of simple phase relations within a discrete quantum system as a result of interactions with an environment. For many applications, the question is not necessarily how to avoid (inevitable)…

In this paper, we consider the initial Neumann boundary value problem for a degenerate kinetic model of Keller--Segel type. The system features a signal-dependent decreasing motility function that vanishes asymptotically, i.e., degeneracies…

Neural agents trained in reinforcement learning settings can learn to communicate among themselves via discrete tokens, accomplishing as a team what agents would be unable to do alone. However, the current standard of using one-hot vectors…

Training agents to communicate with one another given task-based supervision only has attracted considerable attention recently, due to the growing interest in developing models for human-agent interaction. Prior work on the topic focused…

We consider an unsupervised classifying agent that evolves by enforcing self-consistency of its labels under continual exposure to a data-generating environment. Because the agent's predictions feed back into its own regularized updates,…

Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes…

A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…

We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…

This paper introduces a methodology through which a population of autonomous agents can establish a linguistic convention that enables them to refer to arbitrary entities that they observe in their environment. The linguistic convention…

The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic…

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…