CAREER: Sparse Model Selection for Nonlinear Evolution Equations

职业：非线性演化方程的稀疏模型选择

• 批准号: 2331100
• 负责人: Hayden Schaeffer
• 金额: $ 40万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-11-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2331100&HistoricalAwards=false
• 关键词: CAREER; Sparse; Model; Selection; Nonlinear

Extracting information from stationary and/or dynamic data is an important task in many scientific and industrial problems; including but not limited to, machine learning, data mining, image processing, and automated analysis of scientific data. This project focuses on learning the underlying process that generates observational data, in a sense, "reverse-engineering" models from data. These models are often used to gain insights on the data (for example, determining mathematical principles from experimental observations) or to make data-enabled decisions (for example, trend prediction). This is a challenging mathematical and computational problem, since one often has limited information on the process beforehand and real data is often noisy and/or incomplete. The research objective is to construct efficient computational methods for learning generating functions. This will involve a variety of mathematical techniques centered around optimization and sampling theory. The educational objective is to provide advanced training to undergraduate and graduate students in order to prepare them for the U.S. STEM workforce. In particular, students will be mentored and trained through mathematical and computational research projects, collaborative summer programs, working groups, and advanced courses that integrate education and research.The goal is to develop computational methods for model learning, data analysis, and other machine learning tasks. The overall objectives include: (i) the construction of optimization models that use sparsity, smoothness, and randomness to supplement the learning, (ii) the design of efficient and provably convergent numerical methods, (iii) the development of methods that are robust to sample size and outliers, and (iv) the creation and implementation of activities for undergraduate and graduate students that integrate education and research.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.

从固定和/或动态数据中提取信息是许多科学和工业问题的重要任务；包括但不限于机器学习，数据挖掘，图像处理以及对科学数据的自动分析。该项目的重点是学习从数据中产生观察数据的基础过程，从而产生观察数据的“反向工程”模型。这些模型通常用于获得有关数据的见解（例如，从实验观察中确定数学原理）或做出支持数据的决策（例如，趋势预测）。这是一个具有挑战性的数学和计算问题，因为人们通常会事先对该过程的信息有限，而真实数据通常是嘈杂和/或不完整的。研究目标是构建用于学习生成功能的有效计算方法。这将涉及各种围绕优化和采样理论的数学技术。教育目标是为本科生和研究生提供高级培训，以便为美国STEM劳动力做好准备。特别是，将通过数学和计算研究项目，协作夏季计划，工作组以及整合教育和研究的高级课程对学生进行指导和培训。目标是开发用于模型学习，数据分析和其他机器学习任务的计算方法。 总体目标包括：（i）构建优化模型，这些模型使用稀疏性，平稳性和随机性来补充学习，（ii）设计有效且可证明的收敛性数值方法，（iii）开发样本大小和异常值和异常者的稳健性的方法，以及（iv）颁发律师和研究阶段的教育和研究阶段和研究的整体阶段和研究生阶段，并研究了阶段，并研究了阶段和研究的阶段，并研究了阶段和研究的阶段，并构成了阶段和研究的阶段。认为值得通过基金会的智力优点和更广泛影响的评论标准来评估值得支持。