相关论文: Higher-order interaction model from geometric meas…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
Given a network of agents, we study the problem of designing a distributed algorithm that computes k independent weighted means of the network's initial conditions (namely, the agents agree on a k-dimensional space). Akin to average…
This paper considers the consensus problem of a novel opinion dynamics model with group pressure and self-confidence. Different with the most existing paper, the influence of friends of friends in a social network is taken into account,…
Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…
Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
Optical flow is inherently a 2D search problem, and thus the computational complexity grows quadratically with respect to the search window, making large displacements matching infeasible for high-resolution images. In this paper, we take…
In this article, we investigate the asymptotic formation of consensus for several classes of time-dependent cooperative graphon dynamics. After motivating the use of this type of macroscopic models to describe multi-agent systems, we adapt…
Certain consensus seeking multi-agent systems can be formulated as gradient descent flows of a disagreement function. We study how known pathologies of gradient descent flows in Euclidean spaces carry over to consensus seeking systems that…
We consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in…
A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements…
We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…
In this paper, a consensus algorithm is proposed for interacting multi-agents, which can be modeled as simple Mechanical Control Systems (MCS) evolving on a general Lie group. The standard Laplacian flow consensus algorithm for double…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix…
We introduce the problem of asymptotic subspace consensus, which requires the outputs of processes to converge onto a common subspace while remaining inside the convex hull of initial vectors.This is a relaxation of asymptotic consensus in…