Learning Dynamics from Data: Discovering Interaction Laws of Particle and Agent Systems

从数据中学习动力学：发现粒子和代理系统的相互作用规律

• 批准号: 1913243
• 负责人: Fei Lu
• 金额: $ 30万
• 依托单位: Johns Hopkins University
• 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: 2019-08-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913243&HistoricalAwards=false
• 关键词: Learning; Dynamics; Data; Discovering; Interaction

Particle and agent-based systems are ubiquitous in science, for example, particle systems in fundamental physics, agent-based systems that model opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics. To understand the mechanism of these systems, a fundamental challenge is to infer the laws of interaction between the particles and agents from observational data. This project aims to develop mathematical and statistical theory and computationally efficient algorithms for learning these interaction laws from observations in the form of trajectories of the systems. The theory provides performance guarantees and uncertainty quantification in the estimations, therefore providing foundations for model selection and for optimal data collection. The algorithms are scalable to large data sets, avoiding the curse of dimensionality, and are applicable to a wide variety of systems from Physics, Biology, Ecology and Social Sciences.The interaction laws vary largely for different systems, and there is no analytical form in general. The PIs propose non-parametric statistical inference approaches for learning the interaction laws, with no reference or assumption on their analytical form. The research will develop a systematical learning theory for the non-parametric regression of the interaction kernels, whose values are not observed and can not be computed from the data of trajectories of the particles or agents in the system. The theory will study the identifiability of the interaction kernels, the consistency of the estimators, and the optimal choice of hypothesis spaces to achieve optimal rate of convergence of the estimators. With the guidance from the learning theory, we will design computationally efficient algorithms with the following features: (i) avoiding the curse of dimensionality by focusing on the intrinsic dimension of the interaction kernels; (ii) with theoretical guarantee and uncertainty quantification which can be used for model selection and optimal data collection; (iii) scalable to large data sets by implementing in parallel.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.

基于粒子和主体的系统在科学中无处不在，例如，基础物理学中的粒子系统，基于主体的系统，在社会影响下对意见动态进行建模，捕食者-捕食者动态，群集和群集，以及细胞动力学中的趋光性。为了理解这些系统的机制，一个基本的挑战是从观测数据中推断粒子和代理之间的相互作用定律。该项目旨在开发数学和统计理论以及计算效率高的算法，用于从系统轨迹形式的观测中学习这些相互作用定律。该理论提供了性能保证和估计的不确定性量化，从而为模型选择和最佳数据收集提供了基础。该算法可扩展到大数据集，避免了维数灾难，适用于物理学，生物学，生态学和社会科学的各种各样的系统。PI提出了非参数统计推断方法来学习相互作用定律，没有参考或假设其分析形式。该研究将为相互作用核的非参数回归建立一个系统的学习理论，其值不可观测，也无法从系统中粒子或代理的轨迹数据中计算。该理论将研究相互作用核的可识别性，估计量的一致性，以及假设空间的最佳选择，以实现估计量的最佳收敛速度。在学习理论的指导下，我们将设计具有以下特点的计算效率高的算法：（i）通过关注相互作用核的内在维数来避免维数灾难;（ii）具有理论保证和不确定性量化，可用于模型选择和最佳数据收集;（iii）通过并行实施可扩展到大型数据集。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

On the identifiability of interaction functions in systems of interacting particles

• DOI: 10.1016/j.spa.2020.10.005
• 发表时间: 2019-12
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: Zhongyan Li;F. Lu;M. Maggioni;Sui Tang;C. Zhang

Nonparametric inference of interaction laws in systems of agents from trajectory data

从轨迹数据中非参数推断智能体系统中的相互作用规律

• DOI: 10.1073/pnas.1822012116
• 发表时间: 2019
• 期刊: Proceedings of the National Academy of Sciences of the United States of America
• 影响因子: 11.1
• 作者: Lu, Fei;Zhong, Ming;Tang, Sui;Maggioni, Mauro
• 通讯作者: Maggioni, Mauro

Unsupervised learning of observation functions in state space models by nonparametric moment methods

通过非参数矩方法对状态空间模型中的观测函数进行无监督学习

• DOI: 10.3934/fods.2023002
• 发表时间: 2023
• 期刊: Foundations of Data Science
• 影响因子: 2.3
• 作者: An, Qingci;Kevrekidis, Yannis;Lu, Fei;Maggioni, Mauro
• 通讯作者: Maggioni, Mauro

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

学习多轨迹相互作用粒子随机系统中的相互作用核

• DOI: 10.1007/s10208-021-09521-z
• 发表时间: 2021
• 期刊: Foundations of Computational Mathematics
• 影响因子: 3
• 作者: Lu, Fei;Maggioni, Mauro;Tang, Sui
• 通讯作者: Tang, Sui

Learning Interaction Kernels for Agent Systems on Riemannian Manifolds

学习黎曼流形上代理系统的交互内核

• 发表时间: 2021
• 期刊: Proceedings of Machine Learning Research
• 作者: Mauro Maggioni, Jason J