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Sub-Linear Complexity Methods for Multiscale Problems Without Scale Separation

无尺度分离多尺度问题的次线性复杂度方法

基本信息

批准号：
1912999
负责人：
Yoonsang Lee
金额：
$ 9.98万
依托单位：
Dartmouth College
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 2023-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912999&HistoricalAwards=false
关键词：
Sub Linear Complexity Methods Multiscale

项目摘要

Many problems in science and engineering involve complicated interactions between a wide range of scales in space and time, which are computationally challenging to solve for all relevant scales due to a huge simulation cost. The proposed work aims to extract salient features of multiscale problems with a significantly reduced simulation cost. This research will enable fast simulation methods for large-scale computational problems, including optimal design of material properties such as conductivity, elasticity, and long-life cycle of batteries, etc. Also, seismology and acoustic scientific communities will benefit from the proposed work in investigating and studying underground and underwater physics such as object detection, localization, material classification, etc. The project also considers applications in numerical weather forecast methods that significantly improve the prediction accuracy using a large number of samples to quantify uncertainties in the weather forecast models. This project will fund one graduate student in year 2 of the project.The overarching goal of the project is novel sub-linear complexity methods that apply to non-separable multiscale problems. The sub-linear complexity provides a significantly improved efficiency that extracts essential and salient features of the problems without computationally resolving all active scales. The basis of the project is the extraction of effective behaviors through a seamless application of the standard method for separated scale problems. The proposed research offers a unique way to tackle non-separable scale problems without ad-hoc parameter tuning while maintaining a low simulation cost. The mathematical methods to be developed allow judicious applications of the homogenization theory for two-scale problems. Thus, the project has a significant potential to enhance the applicability of the standard computational methods developed for two-scale problems to a wide range of problems. Also, the application and validation in the context of the numerical weather forecast will contribute to connecting deterministic and stochastic multiscale modeling frameworks.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.

科学和工程中的许多问题涉及到空间和时间上各种尺度之间的复杂相互作用，由于巨大的模拟成本，对于所有相关尺度的计算都是具有挑战性的。该工作的目的是在显著降低仿真成本的情况下提取多尺度问题的显著特征。这项研究将使大规模计算问题的快速模拟方法成为可能，包括材料属性的优化设计，如导电性、弹性和电池的长寿命等。此外，地震学和声学科学界将受益于拟议的调查和研究地下和水下物理，如物体探测、定位、材料分类等。该项目还考虑在数值天气预报方法中的应用，通过大量样本量化天气预报模型中的不确定性来显著提高预测精度。这个项目将资助一名研究生在项目的第二年。该项目的总体目标是应用于不可分离的多尺度问题的新颖的亚线性复杂性方法。次线性复杂度显著提高了提取问题的基本和显著特征的效率，而无需通过计算来求解所有活动标度。该项目的基础是通过无缝应用分离规模问题的标准方法来提取有效行为。提出的研究提供了一种独特的方法来解决不可分尺度问题，而无需特别的参数调整，同时保持较低的模拟成本。将要开发的数学方法允许将齐化理论明智地应用于两个尺度的问题。因此，该项目有很大的潜力来提高为两个尺度问题开发的标准计算方法对广泛问题的适用性。此外，在数值天气预报方面的应用和验证将有助于连接确定性和随机多尺度建模框架。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。