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.

该项目的目标是为动力系统开发数据驱动的方法，特别是在不同学科中出现的相互作用的代理/粒子系统和线性扩散过程，例如社会影响下的舆论动态、猎物-捕食者系统、动物的聚集和集群群体、网络上的谣言/威胁传播以及道路网络上的交通流。该项目将重点关注统计学习的想法，以发现控制规律并将观测数据转化为可用于预测的方程。虽然机器学习技术对于这项任务特别有希望，但它们在学习动力系统中的应用仍处于起步阶段。该项目将开发有效的算法，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，以及严格的定量框架来指导选择能够很好地概括未见数据的模型。学生将参与跨学科方面并接受培训。该项目的第一部分涉及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规律，并将其应用于物理、生物学、生态学和社会科学产生的系统，使用机器学习和交互界面的方法。逆问题。将开发系统的学习理论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稳健的方法，从演化状态的部分观察中恢复图上的线性扩散过程，并应用于图信号处理。特别是，该项目将开发采样定理来收集时空样本以及鲁棒的重建算法。采样定理将揭示如何利用图的动力学和图的结构来补偿空间信息的损失。将研究不完美数据造成的影响的理论和算法后果，以在各种图表上的合成和真实数据集上测试所提出的算法。该奖项反映了 NSF 的法定使命，并通过使用基金会的评估进行评估，被认为值得支持。智力价值和更广泛的影响审查标准。

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）

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：
2021-12
期刊：
Inverse Problems
影响因子：
2.1
作者：
Cheng, Jiahui;Tang, Sui
通讯作者：
Tang, Sui

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

推断二阶交互代理系统中交互核的学习理论

DOI：
10.1007/s43670-023-00055-9
发表时间：
2020-10-08
期刊：
Sampling Theory, Signal Processing, and Data Analysis
影响因子：
0
作者：
Jason Miller;Sui Tang;Ming Zhong;M. Maggioni
通讯作者：
M. Maggioni

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

近似原始方程的物理信息神经网络的高阶误差估计

DOI：
10.1007/s42985-023-00254-y
发表时间：
2023-07
期刊：
Partial Differential Equations and Applications
影响因子：
0
作者：
Hu, Ruimeng;Lin, Quyuan;Raydan, Alan;Tang, Sui
通讯作者：
Tang, Sui

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

扩散算子驱动的稀疏带限图信号的时空变密度采样

DOI：
10.1109/icassp49357.2023.10095406
发表时间：
2023-06-04
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：
Sui Tang

An interpretable hybrid predictive model of COVID-19 cases using autoregressive model and LSTM

使用自回归模型和 LSTM 的可解释的 COVID-19 病例混合预测模型