Development of Geometrically-Flexible Physics-Based Convolution Kernels

基于几何灵活物理的卷积核的开发

• 批准号: 2110745
• 负责人: Samy Wu Fung
• 金额: $ 29.76万
• 依托单位: Colorado School of Mines
• 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: 2021-06-15 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110745&HistoricalAwards=false
• 关键词: Development; Geometrically; Flexible; Physics; Based

Data compression is essential in many areas of technology such as satellite imaging, speech recognition, database design, and much more. However, most of this understanding is based on data with good properties.  Increasingly, there is a necessity for techniques that can be applied to complex or incomplete data, so-called flexible data. This project contributes to the development of more advanced compression techniques that can be applied to flexible data.  The main purpose of the project is the development of physics-based computational techniques that enhance data compression algorithms by making them more accurate and efficient.  The ideas developed in this project are applicable to more traditional computational fluid dynamics applications such as hypersonics and atmospheric modeling as well as areas such as machine learning.  In addition to the scientific impact, this project broadens the participation of women in the computational sciences.  It includes support for student mentorship, traineeship, and retention.   The computational skills that the students will obtain are broadly applicable and allows them access to a variety of career options, including in areas of great national need. The PI expects that the tools developed in this proposal will also be included in future outreach talks to the general public.The overall goal of this research is to develop innovative, mathematically rigorous, geometrically flexible, physics-based, multi-dimensional convolution kernels that are useful in areas of data compression, shock filtering, post-processing, and machine learning. The GEOCONKER (GEOmetrically-flexible physics-based CONvolution KERnels) project will not only concentrate on establishing a robust analytical framework, but also on the efficient implementation of these kernels. This will allow for enhancing accurate capturing of multi-scale physics that includes information from sensor data. These techniques will be able to be applied to different types of data and in different manners.   These convolution kernels will aid in establishing provable high-order resolution filters by establishing the interaction between the mathematics, physics, numerics, and geometry in applications.  These novel techniques will use (flexible) spline functions that can adapt to the geometry of the given data on the fly. This will allow for efficient computational codes that will enhance the accurate capturing and filtering of multi-scale physics.  This will include kernels that are useful in shock capturing, accuracy enhancement, and filtering of noisy data. 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.

数据压缩在卫星成像、语音识别、数据库设计等许多技术领域都是必不可少的。然而，这种理解大多是基于具有良好属性的数据。越来越需要能够应用于复杂或不完整数据的技术，即所谓的灵活数据。该项目有助于开发可应用于灵活数据的更先进的压缩技术。该项目的主要目的是开发基于物理的计算技术，通过提高数据压缩算法的准确性和效率来增强它们。该项目开发的思想适用于更传统的计算流体动力学应用，如高超声速和大气建模，以及机器学习等领域。除了科学影响外，该项目还扩大了妇女在计算科学领域的参与。它包括对学生指导、实习和留用的支持。学生将获得广泛适用的计算技能，并使他们能够获得各种职业选择，包括在国家需要的领域。PI期望在该提案中开发的工具也将包括在未来与公众的外联会谈中。本研究的总体目标是开发创新的、数学严谨的、几何灵活的、基于物理的、多维卷积核，这些卷积核在数据压缩、冲击滤波、后处理和机器学习等领域非常有用。GEOCONKER（几何灵活的基于物理的卷积核）项目将不仅专注于建立一个健壮的分析框架，而且还专注于这些核的有效实现。这将允许增强精确捕获多尺度物理，包括来自传感器数据的信息。这些技术将能够以不同的方式应用于不同类型的数据。通过在应用中建立数学、物理、数值和几何之间的相互作用，这些卷积核将有助于建立可证明的高阶分辨率滤波器。这些新技术将使用（灵活的）样条函数，可以适应给定数据的几何形状。这将允许有效的计算代码，将加强准确的捕获和过滤的多尺度物理。这将包括在冲击捕获、精度增强和噪声数据过滤中有用的内核。该奖项反映了美国国家科学基金会的法定使命，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。