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

• 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

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.

该项目的目标是为动态系统开发数据驱动的方法，特别是在交互代理/粒子系统和线性扩散过程中出现的各种学科，如社会影响下的意见动态，捕食者系统，动物群体的群集和群集，网络上的谣言/威胁传播，以及道路网络上的交通流量。 该项目将侧重于统计学习的想法，以发现支配定律，并将观测数据转化为可用于预测的方程。虽然机器学习技术在这方面特别有前途，但它们在学习动态系统方面的应用仍处于起步阶段。该项目将开发有效的算法，以从各种类型的观测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，以指导模型的选择，这些模型可以很好地概括看不见的数据。学生将参与并接受跨学科方面的培训。该项目的第一部分涉及基于回归的学习方法，以发现来自各种类型轨迹数据的代理之间的交互规律，并应用于物理学，生物学，生态学和社会科学的系统，使用机器学习和逆问题的接口方法。系统的学习理论将被开发来研究适定性和模型选择，以实现统计上的最佳性能。该项目的第二部分将开发强大的方法来恢复线性扩散过程的图形从部分观测的演变状态，与图形信号处理的应用程序。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动态图和图的结构，以补偿空间信息的损失。不完善的数据所造成的影响的理论和算法的分支将被研究，以测试合成和真实的数据集在各种各样的graphs.This奖项的建议算法反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

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)
• 作者: Qing Yao;Longxiu Huang;Sui Tang

Learning theory for inferring interaction kernels in second-order interacting agent systems

• DOI: 10.1007/s43670-023-00055-9
• 发表时间: 2020-10
• 期刊: Sampling Theory, Signal Processing, and Data Analysis
• 作者: Jason Miller;Sui Tang;Ming Zhong;M. Maggioni

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

• DOI: 10.51387/22-nejsds13
• 发表时间: 2022-03
• 期刊: The New England Journal of Statistics in Data Science
• 作者: Mengyang Gu;Xubo Liu;X. Fang;Sui Tang

Higher-order error estimates for physics-informed neural networks approximating the primitive equations

• DOI: 10.1007/s42985-023-00254-y
• 发表时间: 2022-09
• 期刊: Partial Differential Equations and Applications
• 作者: Ruimeng Hu;Quyuan Lin;Alan Raydan;Sui Tang

Estimate the spectrum of affine dynamical systems from partial observations of a single trajectory data

根据单个轨迹数据的部分观测来估计仿射动力系统的谱

• DOI: 10.1088/1361-6420/ac37fb
• 发表时间: 2021
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: Cheng, Jiahui;Tang, Sui
• 通讯作者: Tang, Sui