1,950 research outputs found
An Eulerian Approach to the Analysis of Krause's Consensus Models
Abstract. In this paper we analyze a class of multi-agent consensus dynamical systems inspired by Krauseās original model. As in Krauseās, the basic assumption is the so-called bounded confidence: two agents can influence each other only when their state values are below a given distance threshold R. We study the system under an Eulerian point of view considering (possibly continuous) probability distributions of agents and we present original convergence results. The limit distribution is always necessarily a convex combination of delta functions at least R far apart from each other: in other terms these models are locally aggregating. The Eulerian perspective provides the natural framework for designing a numerical algorithm, by which we obtain several simulations in 1 and 2 dimensions
How Bad is Forming Your Own Opinion?
The question of how people form their opinion has fascinated economists and
sociologists for quite some time. In many of the models, a group of people in a
social network, each holding a numerical opinion, arrive at a shared opinion
through repeated averaging with their neighbors in the network. Motivated by
the observation that consensus is rarely reached in real opinion dynamics, we
study a related sociological model in which individuals' intrinsic beliefs
counterbalance the averaging process and yield a diversity of opinions.
By interpreting the repeated averaging as best-response dynamics in an
underlying game with natural payoffs, and the limit of the process as an
equilibrium, we are able to study the cost of disagreement in these models
relative to a social optimum. We provide a tight bound on the cost at
equilibrium relative to the optimum; our analysis draws a connection between
these agreement models and extremal problems that lead to generalized
eigenvalues. We also consider a natural network design problem in this setting:
which links can we add to the underlying network to reduce the cost of
disagreement at equilibrium
Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies
From a perspective of designing or engineering for opinion formation games in
social networks, the "opinion maximization (or minimization)" problem has been
studied mainly for designing subset selecting algorithms. We furthermore define
a two-player zero-sum Stackelberg game of competitive opinion optimization by
letting the player under study as the first-mover minimize the sum of expressed
opinions by doing so-called "internal opinion design", knowing that the other
adversarial player as the follower is to maximize the same objective by also
conducting her own internal opinion design.
We propose for the min player to play the "follow-the-perturbed-leader"
algorithm in such Stackelberg game, obtaining losses depending on the other
adversarial player's play. Since our strategy of subset selection is
combinatorial in nature, the probabilities in a distribution over all the
strategies would be too many to be enumerated one by one. Thus, we design a
randomized algorithm to produce a (randomized) pure strategy. We show that the
strategy output by the randomized algorithm for the min player is essentially
an approximate equilibrium strategy against the other adversarial player
CFDNet: a deep learning-based accelerator for fluid simulations
CFD is widely used in physical system design and optimization, where it is
used to predict engineering quantities of interest, such as the lift on a plane
wing or the drag on a motor vehicle. However, many systems of interest are
prohibitively expensive for design optimization, due to the expense of
evaluating CFD simulations. To render the computation tractable, reduced-order
or surrogate models are used to accelerate simulations while respecting the
convergence constraints provided by the higher-fidelity solution. This paper
introduces CFDNet -- a physical simulation and deep learning coupled framework,
for accelerating the convergence of Reynolds Averaged Navier-Stokes
simulations. CFDNet is designed to predict the primary physical properties of
the fluid including velocity, pressure, and eddy viscosity using a single
convolutional neural network at its core. We evaluate CFDNet on a variety of
use-cases, both extrapolative and interpolative, where test geometries are
observed/not-observed during training. Our results show that CFDNet meets the
convergence constraints of the domain-specific physics solver while
outperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows.
Moreover, we demonstrate the generalization capacity of CFDNet by testing its
prediction on new geometries unseen during training. In this case, the approach
meets the CFD convergence criterion while still providing significant speedups
over traditional domain-only models.Comment: It has been accepted and almost published in the International
Conference in Supercomputing (ICS) 202
Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents
We present a novel method for guiding a large-scale swarm of autonomous
agents into a desired formation shape in a distributed and scalable manner. Our
Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC)
algorithm adopts an Eulerian framework, where the physical space is partitioned
into bins and the swarm's density distribution over each bin is controlled.
Each agent determines its bin transition probabilities using a
time-inhomogeneous Markov chain. These time-varying Markov matrices are
constructed by each agent in real-time using the feedback from the current
swarm distribution, which is estimated in a distributed manner. The PSG-IMC
algorithm minimizes the expected cost of the transitions per time instant,
required to achieve and maintain the desired formation shape, even when agents
are added to or removed from the swarm. The algorithm scales well with a large
number of agents and complex formation shapes, and can also be adapted for area
exploration applications. We demonstrate the effectiveness of this proposed
swarm guidance algorithm by using results of numerical simulations and hardware
experiments with multiple quadrotors.Comment: Submitted to IEEE Transactions on Robotic
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