Data-Driven Discovery of Dynamics in Interacting Agent Systems and Linear Diffusion Processes

交互代理系统和线性扩散过程中的数据驱动动力学发现

基本信息

批准号：
2111303
负责人：
Sui Tang
金额：
$ 20万
依托单位：
University of California-Santa Barbara
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-08-15 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111303&HistoricalAwards=false
关键词：
Data Driven Discovery Dynamics Interacting

项目摘要

The goal of this project is to develop data-driven methods for dynamical systems and specifically on interacting agent/particle systems and linear diffusion processes that arise in various disciplines such as opinion dynamics under social influence, prey-predator systems, flocking and swarming of animal groups, rumor/threat propagations over networks, and traffic flow over road networks. The project will focus on ideas from statistical learning for the discovery of governing laws and turning the observational data into equations that can be used for predictions. While machine learning techniques are particularly promising for this task their application to learning dynamical systems is still in its infancy. This project will develop efficient algorithms to learn unknown structures and parameters of the systems from various types of observational trajectory data, together with a rigorous quantitative framework to guide the selection of models that generalize well on unseen data. Students will be involved and trained in interdisciplinary aspects. The first part of the project addresses regression-based learning approaches to discover interaction laws between agents from various types of trajectory data, with applications to systems arising from physics, biology, ecology, and social sciences, using methods at the interface of machine learning and inverse problems. Systematic learning theories will be developed to study the well-posedness and model selections to achieve statistically optimal performance. The second part of the project will develop robust methods to recover linear diffusion processes over graphs from partial observations of evolving states, with applications to graph signal processing. In particular the project will develop sampling theorems to collect space-time samples as well as robust reconstruction algorithms. The sampling theorems will shed light on how to utilize dynamics over graphs and the structure of graphs to compensate for the loss of spatial information. Theoretical and algorithmic ramifications of the effects caused by imperfect data will be studied to test the proposed algorithms on synthetic and real data sets over a wide variety of graphs.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.

该项目的目的是开发动态系统的数据驱动方法，特别是在各种学科中出现的相互作用的代理/粒子系统和线性扩散过程，例如在社会影响力，猎物pre依者系统，动物群体的群体和群体下的舆论动态，谣言/威胁性的谣言/威胁性繁殖网络以及流量上流动的网络网络。该项目将重点关注统计学习的思想，以发现管理法律，并将观察数据变成可用于预测的方程式。尽管机器学习技术对于这项任务特别有希望，但他们在学习动态系统中的应用仍处于起步阶段。该项目将开发有效的算法，以从各种类型的观察轨迹数据中学习系统的未知结构和参数，以及一个严格的定量框架，以指导在看不见的数据上概括的模型的选择。学生将参与并接受跨学科方面的培训。该项目的第一部分介绍了基于回归的学习方法，以从各种类型的轨迹数据中发现代理之间的相互作用定律，并使用机器学习和反相反问题的界面上的方法应用于物理，生物学，生态学和社会科学的系统。将开发系统的学习理论，以研究适合和模型的选择，以实现统计学上最佳的性能。该项目的第二部分将开发出可靠的方法，以从不断发展的状态的部分观察结果中恢复图形上的线性扩散过程，并应用于图形信号处理。特别是该项目将开发采样定理以收集时空样本以及强大的重建算法。采样定理将阐明如何利用图表上的动力学和图形结构来补偿空间信息的丢失。将研究由不完美数据引起的效果的理论和算法分析，以测试有关综合和真实数据集的拟议算法，这些算法在各种图形上进行。该奖项反映了NSF的法定任务，并认为通过基金会的知识分子和更广泛的影响，通过评估来评估，这是值得的。

项目成果

期刊论文数量（8）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Space-Time Variable Density Samplings for Sparse Bandlimited Graph Signals Driven by Diffusion Operators

DOI：
10.1109/icassp49357.2023.10095406
发表时间：
2023-06
期刊：
ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
影响因子：
0
作者：
Qing Yao;Longxiu Huang;Sui Tang
通讯作者：
Qing Yao;Longxiu Huang;Sui Tang

Scalable Marginalization of Correlated Latent Variables with Applications to Learning Particle Interaction Kernels