Quantifying Chaos, Correlations, and Oscillations in Multi-Agent Systems and Advection Equations

量化多智能体系统和平流方程中的混沌、相关性和振荡

基本信息

批准号：
1908739
负责人：
Pierre-Emmanuel Jabin
金额：
$ 38.3万
依托单位：
University of Maryland, College Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-15 至 2020-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1908739&HistoricalAwards=false
关键词：
Quantifying Chaos Correlations Oscillations Multi

项目摘要

The project studies transport and advection equations with applications in the Biosciences, Statistical Physics and Fluid Mechanics. A first guiding example for the research includes large systems of interacting "agents" or "particles" that have long been employed in Physics: in Astrophysics to predict the evolution in time of galaxies or galaxy clusters to try to understand how they are formed, in plasmas to describe the dynamics of ions and electrons in plasmas, to model the behavior of air bubbles in water or other small objects in a fluid. In addition, such large systems are now widely used in Biology to model the motion of micro-organisms ("particles" can then be cells in the human body), in Finance and Economics, and other Social Sciences. A second guiding set of examples is composed of various fluid models (liquid or gas) which can exhibit complex compressive effects commonly found in geophysical (oceans or atmosphere) or biological settings. The project aims at deriving and validating effective models: By reducing the complexity of large systems of agents/particles through the so-called mean-field limit, or by controlling the behavior of effective state laws in Fluid Mechanics that are a priori unstable.The models investigated in this research all employ transport equations: non-linear convection systems in low dimension for compressible fluids, the linear Liouville equation in very large dimension for simple multi-agent systems but more also more complex non-linear equations (such as Hamilton-Jacobi-Bellman) for systems with control. The project focuses in particular on systems that are unstable or singular and are expected to create or amplify correlations and oscillations. A key unifying question in the research is to identify the critical scale in the models to quantify how those correlations or oscillations may develop. For large systems of particles, the project makes use of explicit estimates involving the rescaled relative entropy, renormalized to include the comparisons between the Gibbs equilibria. For convective models, the project introduces new semi-norms which precisely track the possible oscillations in the density at the critical log or log log scales.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目研究输运和平流方程及其在生物科学、统计物理和流体力学中的应用。该研究的第一个指导性例子包括长期在物理学中使用的相互作用“代理”或“粒子”的大型系统：在天体物理学中预测星系或星系团随时间的演化，以试图了解它们是如何形成的，在等离子体来描述等离子体中离子和电子的动力学，模拟水中气泡或流体中其他小物体的行为。此外，这种大型系统现在广泛应用于生物学、金融和经济学以及其他社会科学领域，以模拟微生物的运动（“粒子”可以是人体中的细胞）。第二组指导示例由各种流体模型（液体或气体）组成，这些模型可以表现出地球物理（海洋或大气）或生物环境中常见的复杂压缩效应。该项目旨在推导和验证有效的模型：通过所谓的平均场极限降低大型代理/粒子系统的复杂性，或者通过控制先验不稳定的流体力学中有效状态定律的行为。本研究中研究的模型都采用传输方程：可压缩流体的低维非线性对流系统，简单多智能体系统的大维线性刘维尔方程，但也有更复杂的非线性方程（例如Hamilton-Jacobi-Bellman）用于带控制的系统。该项目特别关注不稳定或奇异的系统，并预计会产生或放大相关性和振荡。研究中的一个关键统一问题是确定模型中的临界尺度，以量化这些相关性或振荡可能如何发展。对于大型粒子系统，该项目利用涉及重新调整的相对熵的显式估计，重新归一化以包括吉布斯平衡之间的比较。对于对流模型，该项目引入了新的半范数，可以精确跟踪临界对数或对数对数尺度上密度可能的振荡。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势和评估进行评估，被认为值得支持。更广泛的影响审查标准。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Transport model for feature extraction.

用于特征提取的传输模型。

DOI：
发表时间：
2021-01
期刊：
SIAM journal on mathematics of data science
影响因子：
0
作者：
Czaja, W.;Dong, D.;Jabin, P.;Njeunje, F. O.
通讯作者：
Njeunje, F. O.

Memory-driven movement model for periodic migrations

用于周期性迁移的内存驱动运动模型

DOI：
发表时间：
2021-01
期刊：
Journal of theoretical biology
影响因子：
2
作者：
Lin, H.;Fagan, W. F.;Jabin, P.
通讯作者：
Jabin, P.

Analysis of Hyperspectral Data by Means of Transport Models and Machine Learning

通过传输模型和机器学习分析高光谱数据

DOI：
10.1109/igarss39084.2020.9323215
发表时间：
2020-09-26
期刊：
IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium
影响因子：
0
作者：
W. Czaja;Dong Dong;P. Jabin;Franck Olivier Ndjakou Njeunje
通讯作者：
Franck Olivier Ndjakou Njeunje

Local regularity result for an optimal transportation problem with rough measures in the plane.

局部规律性导致了平面上粗略措施的最优运输问题。