Collaborative Research: Stochastic Methods for Complex Systems
合作研究:复杂系统的随机方法
基本信息
- 批准号:1818716
- 负责人:
- 金额:$ 9.81万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-08-01 至 2022-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project addresses computational challenges in materials science, chemistry, uncertainty quantification, and related fields. Quantities of interest such as chemical reaction rates, strength of alloys, and more, can be estimated using a common mathematical modeling framework that computes mean values and provides quantification of the variance about the means. Estimating these quantities by computer simulation can be particularly challenging when the property that one wishes to study is rare and many repeated computer simulations would be required to estimate the mean value and the variance. While this challenge is somewhat alleviated by growth in computing power, some simulations, including chemical reaction rates, cannot be addressed via brute force computation. Rather than rely on raw computing power, the investigators intend to develop novel computer algorithms and approximations that will allow for more efficient and more accurate predictions. This includes the use of interacting copies of mathematical models, which communicate information between one another, resulting in higher quality estimates. These algorithms and approximations will allow more faithful prediction of quantities of interest and access to bigger models (such as larger, more complicated molecules). Mathematically the project will provide a rigorous understanding of the computer algorithms, providing confidence to scientists in a variety of fields. Multiscale distributions appear in a variety of applications, including materials science, chemistry, and uncertainty quantification. Given efficient sampling strategies, one can compute a variety of quantities of interest, including ensemble averages, mean first passage times, and probabilities of rare events. However, multiscale distributions in high number of dimensions are particularly challenging to sample. One example is the Boltzmann distribution induced by an energy landscape containing superbasins. Such a landscape features clusters of local minima that correspond to close groupings of modes in the distribution. This project will investigate four sampling algorithms: weighted ensemble sampling, parallel replica dynamics, local entropy smoothing, and piecewise deterministic Markov processes. Weighted ensemble sampling partitions state space into bins and then elects to sample within those bins in an optimal way. The project will investigate the choice of the sample allocation strategy and consider both finite and infinite system size limits for the method. Parallel replica dynamics also involves using an ensemble of samples, but, in contrast to weighted ensemble, it uses the replicas to efficiently find first exits out of one metastable region and into another. Local entropy smoothing removes the superbasin features of the energy landscape by performing local ensemble sampling and averaging. Finally, the investigators will use piecewise deterministic Markov processes to perform rejection free sampling without requiring estimates of gradients. These algorithms will be rigorously analyzed, and they will be tested on a variety of realistic high-dimensional problems including chemical reaction networks and stochastic molecular dynamics.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.
这个项目解决了材料科学、化学、不确定度量化和相关领域的计算挑战。可以使用通用的数学建模框架来估计感兴趣的数量,如化学反应速率、合金强度等,该框架计算平均值并提供关于平均值的方差的量化。当人们希望研究的性质很少,并且需要多次重复的计算机模拟来估计平均值和方差时,通过计算机模拟来估计这些量可能特别具有挑战性。虽然计算能力的增长在一定程度上缓解了这一挑战,但一些模拟,包括化学反应速率,不能通过蛮力计算来解决。研究人员不再依赖原始的计算能力,而是打算开发新的计算机算法和近似,以实现更高效、更准确的预测。这包括使用数学模型的交互副本,这些模型彼此之间交流信息,从而产生更高质量的估计。这些算法和近似将允许更准确地预测感兴趣的数量,并获得更大的模型(如更大、更复杂的分子)。在数学上,该项目将提供对计算机算法的严格理解,为不同领域的科学家提供信心。多尺度分布出现在各种应用中,包括材料科学、化学和不确定性量化。给出有效的抽样策略,人们可以计算各种感兴趣的量,包括总体平均值、平均首次通过时间和罕见事件的概率。然而,高维的多尺度分布对抽样特别具有挑战性。一个例子是由包含超级盆地的能量景观引起的玻尔兹曼分布。这样的景观以对应于分布中的模式的紧密分组的局部极小的集群为特征。本项目将研究四种采样算法:加权集成采样、并行复制动态、局部熵平滑和分段确定性马尔可夫过程。加权集成采样将状态空间划分为箱,然后选择以最优方式在这些箱中采样。该项目将调查样本分配策略的选择,并考虑该方法的有限和无限系统大小限制。并行复制动力学还涉及使用样本集成,但与加权集成相比,它使用复制来有效地找到从一个亚稳定区域到另一个亚稳定区域的第一个出口。局部熵平滑通过执行局部集合采样和平均来去除能量景观的超盆地特征。最后,研究人员将使用分段确定性马尔可夫过程来执行无拒收抽样,而不需要估计梯度。这些算法将经过严格的分析,并将在各种现实的高维问题上进行测试,包括化学反应网络和随机分子动力学。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。
项目成果
期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Relative entropy minimization over Hilbert spaces via Robbins-Monro
通过 Robbins-Monro 实现希尔伯特空间上的相对熵最小化
- DOI:10.3934/math.2019.3.359
- 发表时间:2019
- 期刊:
- 影响因子:2.2
- 作者:Simpson, Gideon;Watkins, Daniel
- 通讯作者:Watkins, Daniel
Iterate averaging, the Kalman filter, and 3DVAR for linear inverse problems
- DOI:10.1007/s11075-022-01332-9
- 发表时间:2021-10
- 期刊:
- 影响因子:2.1
- 作者:Felix G. Jones;G. Simpson
- 通讯作者:Felix G. Jones;G. Simpson
Sampling from rough energy landscapes
- DOI:10.4310/cms.2020.v18.n8.a9
- 发表时间:2019-03
- 期刊:
- 影响因子:1
- 作者:P. Plech'avc;G. Simpson
- 通讯作者:P. Plech'avc;G. Simpson
Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
- DOI:10.1063/1.5120511
- 发表时间:2019-11-07
- 期刊:
- 影响因子:4.4
- 作者:Copperman, Jeremy;Aristoff, David;Zuckerman, Daniel M.
- 通讯作者:Zuckerman, Daniel M.
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Gideon Simpson其他文献
Unbiased Trajectory-Based Estimation of Stationary Distributions and Splitting Probabilities
- DOI:
10.1016/j.bpj.2020.11.1239 - 发表时间:
2021-02-12 - 期刊:
- 影响因子:
- 作者:
John D. Russo;David Aristoff;Gideon Simpson;Jeremy T. Copperman;Daniel M. Zuckerman - 通讯作者:
Daniel M. Zuckerman
Iterative steady state restarting to accelerate weighted ensemble convergence
- DOI:
10.1016/j.bpj.2021.11.1375 - 发表时间:
2022-02-11 - 期刊:
- 影响因子:
- 作者:
John Russo;Jeremy T. Copperman;David Aristoff;Gideon Simpson;Daniel M. Zuckerman - 通讯作者:
Daniel M. Zuckerman
Data-driven variance reduction in weighted ensemble simulations
- DOI:
10.1016/j.bpj.2023.11.2568 - 发表时间:
2024-02-08 - 期刊:
- 影响因子:
- 作者:
Won Hee Ryu;John D. Russo;Mats S. Johnson;Jeffrey P. Thompson;David N. LeBard;Gideon Simpson;David Aristoff;Robert J. Webber;Jeremy T. Copperman;Daniel M. Zuckerman - 通讯作者:
Daniel M. Zuckerman
A multiscale model of partial melts: 2. Numerical results
部分熔化的多尺度模型:2.数值结果
- DOI:
- 发表时间:
2009 - 期刊:
- 影响因子:0
- 作者:
Gideon Simpson;M. Spiegelman;M. I. Weinstein - 通讯作者:
M. I. Weinstein
Minimizing variance of reaction rate estimation in weighted ensemble simulation using synthetic molecular dynamics
- DOI:
10.1016/j.bpj.2022.11.2289 - 发表时间:
2023-02-10 - 期刊:
- 影响因子:
- 作者:
Won Hee Ryu;John Russo;Mats S. Johnson;Jeffrey P. Thompson;David N. LeBard;Gideon Simpson;David Aristoff;Robert J. Webber;Jeremy T. Copperman;Daniel M. Zuckerman - 通讯作者:
Daniel M. Zuckerman
Gideon Simpson的其他文献
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{{ truncateString('Gideon Simpson', 18)}}的其他基金
Collaborative Research: Particles and Proxies for Sampling
协作研究:采样的粒子和代理
- 批准号:
2111278 - 财政年份:2021
- 资助金额:
$ 9.81万 - 项目类别:
Standard Grant
Computational and Analytical Challenges in Nonlinear Dispersive Wave Equations
非线性色散波动方程的计算和分析挑战
- 批准号:
1409018 - 财政年份:2014
- 资助金额:
$ 9.81万 - 项目类别:
Continuing Grant
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Cell Research
- 批准号:31224802
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Cell Research
- 批准号:31024804
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Cell Research (细胞研究)
- 批准号:30824808
- 批准年份:2008
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- 批准号:10774081
- 批准年份:2007
- 资助金额:45.0 万元
- 项目类别:面上项目
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