Novel Numerical Methods for Nonlinear Stochastic PDEs and High Dimensional Computation

非线性随机偏微分方程和高维计算的新数值方法

基本信息

  • 批准号:
    2309626
  • 负责人:
  • 金额:
    $ 37.96万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2023
  • 资助国家:
    美国
  • 起止时间:
    2023-08-01 至 2026-07-31
  • 项目状态:
    未结题

项目摘要

Many scientific, engineering, and industrial applications involve random effects. Incorporating uncertainties into mathematical models becomes indispensable in order to develop more accurate and robust mathematical models from biological, engineering, and physical applications, which makes it necessary to consider stochastic partial differential equations as they are the most commonly encountered stochastic models from applications. To seek solutions of those equations require accurate, efficient, and robust computational methods and algorithms, the demand for such methods and algorithms has never been greater. The current approaches for solving stochastic partial differential equations face considerable challenges at large scales, in the meantime, such stochastic models become more complicated as more difficult nonlinearity and noise are considered. The existing numerical approaches are not efficient to solve those problems, which in turn calls for new ideas and approaches. With rapid developments in nontraditional applied sciences such as mathematical finance, image processing, economics, and data science, there is an ever-increasing demand for efficient numerical methods for solving challenging high-dimensional problems such as computing integration and solving partial differential equations. The traditional grid-based methods are hampered by the infamous curse of dimensionality in which the amount of required computations for solving a problem grows exponentially in the dimension. The primary goal of this research project is to develop novel and efficient numerical methods to address those challenges. The project consists of two integral parts. Part I focuses on developing and analyzing efficient numerical methods for solving several nonlinear stochastic partial differential equations which arise from various scientific and engineering applications such as materials science, fluid and quantum mechanics, and optimal control. Part II will be devoted to developing novel numerical methods for high-dimensional computation with a focus on problems of high-dimensional numerical integration and high-dimensional partial differential equations. The overreaching vision of this project is to develop a framework for constructing and analyzing numerical methods for general nonlinear stochastic partial differential equations and to develop new approaches and enabling methods for overcoming the curse of dimensionality challenge for high-dimensional computation. The project will include training of graduate students.This research project develops advanced numerical methods for nonlinear stochastic partial differential equations and high-dimensional computation. Such a timely and advanced project is of great interest to the STEM community as the anticipated numerical methods and algorithms will provide much-needed enabling tools for tackling challenging problems described mathematically by stochastic partial differential equations or involved with high-dimensional computation from many scientific, engineering, and industrial applications as well as AI, machine learning, and data science. This research project is also expected to have a lasting impact on the advancement of numerical stochastic partial differential equations and high-dimensional computation. Moreover, the project will provide a valuable opportunity and resource to train Ph.D. graduate students and to help them to develop necessary applied and computational mathematics as well as AI, machine learning, and data science knowledge and skills so that they can pursue successful careers in either academia or industry in the near future.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.
许多科学、工程和工业应用都涉及随机效应。为了从生物、工程和物理应用中开发更精确和鲁棒的数学模型,将不确定性纳入数学模型变得不可或缺,这使得有必要考虑随机偏微分方程,因为它们是应用中最常见的随机模型。为了寻求这些方程的解,需要准确、高效和鲁棒的计算方法和算法,对此类方法和算法的需求从未如此之大。目前求解随机偏微分方程的方法在大尺度上面临着相当大的挑战,同时,随着非线性和噪声的增加,这类随机模型变得更加复杂。现有的数值方法不能有效解决这些问题,这就需要新的思路和方法。随着金融数学、图像处理、经济学和数据科学等非传统应用科学的快速发展,人们越来越需要高效的数值方法来解决具有挑战性的高维问题,如计算积分和求解偏微分方程。传统的基于网格的方法受到臭名昭著的维数灾难的阻碍,其中解决问题所需的计算量在维度上呈指数级增长。该研究项目的主要目标是开发新颖有效的数值方法来应对这些挑战。该项目由两个组成部分组成。第一部分着重于开发和分析有效的数值方法来解决几个非线性随机偏微分方程所产生的各种科学和工程应用,如材料科学,流体和量子力学,最优控制。第二部分将致力于开发新的数值方法,高维计算的重点是高维数值积分和高维偏微分方程的问题。该项目的超越愿景是开发一个框架,用于构建和分析一般非线性随机偏微分方程的数值方法,并开发新的方法和使能方法,以克服高维计算的维数灾难挑战。本研究课题为非线性随机偏微分方程和高维计算的高级数值方法的开发。这样一个及时和先进的项目是STEM社区的极大兴趣,因为预期的数值方法和算法将提供急需的使能工具,用于解决由随机偏微分方程数学描述的具有挑战性的问题,或涉及许多科学,工程和工业应用以及人工智能,机器学习和数据科学的高维计算。该研究项目也有望对数值随机偏微分方程和高维计算的进步产生持久的影响。此外,该项目将为培养博士生提供宝贵的机会和资源。研究生,并帮助他们发展必要的应用和计算数学以及人工智能,机器学习和数据科学知识和技能,使他们能够在不久的将来在学术界或工业界追求成功的职业生涯。该奖项反映了NSF的法定使命,并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Xiaobing Feng其他文献

DNNTune: Automatic Benchmarking DNN Models for Mobile-cloud Computing
DNNTune:移动云计算 DNN 模型的自动基准测试
Associations of urinary 1,3-butadiene metabolite with glucose homeostasis, prediabetes, and diabetes in the US general population: Role of alkaline phosphatase.
美国普通人群尿 1,3-丁二烯代谢物与葡萄糖稳态、糖尿病前期和糖尿病的关联:碱性磷酸酶的作用。
  • DOI:
    10.1016/j.envres.2023.115355
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    8.3
  • 作者:
    Ruyi Liang;Xiaobing Feng;Da Shi;Linling Yu;Meng Yang;Min Zhou;Yongfang Zhang;Bin Wang;Weihong Chen
  • 通讯作者:
    Weihong Chen
Depth Camera Based Fluid Reconstruction and its Solid-fluid Interaction
基于深度相机的流体重建及其固液相互作用
CloudRaid: Detecting Distributed Concurrency Bugs via Log Mining and Enhancement
CloudRaid:通过日志挖掘和增强检测分布式并发错误
  • DOI:
    10.1109/tse.2020.2999364
  • 发表时间:
    2022-02
  • 期刊:
  • 影响因子:
    7.4
  • 作者:
    Jie Lu;Feng Li;Chen Liu;Lian Li;Xiaobing Feng;Jingling Xue
  • 通讯作者:
    Jingling Xue
Cascade Wide Activation Multi-Scale Networks for Single Image Super-Resolution
用于单图像超分辨率的级联宽激活多尺度网络

Xiaobing Feng的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Xiaobing Feng', 18)}}的其他基金

Efficient Numerical Methods and Algorithms for Nonlinear Stochastic Partial Differential Equations
非线性随机偏微分方程的高效数值方法和算法
  • 批准号:
    2012414
  • 财政年份:
    2020
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Novel numerical methods for fully nonlinear second order elliptic and parabolic Monge-Ampere and Hamilton-Jacobi-Bellman equations
全非线性二阶椭圆和抛物线 Monge-Ampere 和 Hamilton-Jacobi-Bellman 方程的新颖数值方法
  • 批准号:
    1620168
  • 财政年份:
    2016
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Continuing Grant
Novel Discontinuous Galerkin Finite Element Methods for Second Order Fully Nonlinear Equations and High Frequency Wave Equations
二阶完全非线性方程和高频波动方程的新型间断伽辽金有限元方法
  • 批准号:
    1318486
  • 财政年份:
    2013
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Conference: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
会议:偏微分方程不连续伽辽金有限元方法的最新进展
  • 批准号:
    1203237
  • 财政年份:
    2012
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Numerical Methods and Algorithms for Fully Nonlinear Second Order Evolution Equations with Applications
全非线性二阶演化方程的数值方法和算法及其应用
  • 批准号:
    1016173
  • 财政年份:
    2010
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Continuing Grant
Numerical Methods and Algorithms for Second Order Fully Nonlinear Partial Differential Equations
二阶完全非线性偏微分方程的数值方法和算法
  • 批准号:
    0710831
  • 财政年份:
    2007
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
International Workshop on Computational Methods in Geosciences
地球科学计算方法国际研讨会
  • 批准号:
    0715713
  • 财政年份:
    2007
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Computational Challenges in Geometrical Flows: Numerical Methods and Analysis, Algorithmic Development and Software Engineering
几何流中的计算挑战:数值方法和分析、算法开发和软件工程
  • 批准号:
    0410266
  • 财政年份:
    2004
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
The Barrett Lectures May, 2001 "New Directions and Developments in Computational Mathematics
巴雷特讲座,2001 年 5 月“计算数学的新方向和发展
  • 批准号:
    0107159
  • 财政年份:
    2001
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant

相似海外基金

A novel development of optimization and deep learning methods based on the idea of structure-preserving numerical analysis
基于结构保持数值分析思想的优化和深度学习方法的新发展
  • 批准号:
    21H03452
  • 财政年份:
    2021
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Novel Methods for Numerical Simulation of Wave Propagation in Inhomogeneous Media
非均匀介质中波传播数值模拟的新方法
  • 批准号:
    2110407
  • 财政年份:
    2021
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Novel Decompositions and Fast Numerical Methods for Peridynamics
近场动力学的新颖分解和快速数值方法
  • 批准号:
    2108588
  • 财政年份:
    2021
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Standard Grant
Novel mathematics and numerical methods for ferromagnetic problems
铁磁问题的新颖数学和数值方法
  • 批准号:
    DP190101197
  • 财政年份:
    2019
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Discovery Projects
Novel physical and numerical methods for simulating water and heat transfer in land surface models.
用于模拟地表模型中水和热传递的新颖物理和数值方法。
  • 批准号:
    2202955
  • 财政年份:
    2019
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Studentship
Novel physical and numerical methods for simulating water, heat and gas transfer in land surface models, with focus on UKMO JULES model
用于模拟地表模型中水、热和气体传递的新颖物理和数值方法,重点是 UKMO JULES 模型
  • 批准号:
    NE/R008469/1
  • 财政年份:
    2019
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Training Grant
Novel numerical methods for emerging additive manufacturing technology of Organic-Light Emitting Diodes O-LED
有机发光二极管 O-LED 新兴增材制造技术的新颖数值方法
  • 批准号:
    1972026
  • 财政年份:
    2017
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Studentship
The combination of numerical methods from a novel linear transformation model and laser diagnostic methods for the characterisation of laminar flames
将新型线性变换模型的数值方法与激光诊断方法相结合来表征层流火焰
  • 批准号:
    397116102
  • 财政年份:
    2017
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Research Fellowships
Novel Numerical Methods for Additive Manufacturing 3D Printing of Dissimilar Materials
异种材料增材制造 3D 打印的新颖数值方法
  • 批准号:
    1823167
  • 财政年份:
    2016
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Studentship
Novel numerical methods for fully nonlinear second order elliptic and parabolic Monge-Ampere and Hamilton-Jacobi-Bellman equations
全非线性二阶椭圆和抛物线 Monge-Ampere 和 Hamilton-Jacobi-Bellman 方程的新颖数值方法
  • 批准号:
    1620168
  • 财政年份:
    2016
  • 资助金额:
    $ 37.96万
  • 项目类别:
    Continuing Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了