Development of time-parallel numerical integration algorithms using probabilistic methods with applications to magnetic fusion plasma.

使用概率方法开发时间并行数值积分算法并应用于磁聚变等离子体。

• 批准号: 2271223
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2271223
• 关键词: Development; time; parallel; numerical; integration

The context of the research - In many branches of science, from astrophysics to epidemiology, mathematical and computational modelling is vital and often involves the numerical integration of large systems of differential equations. Many simulations are limited by bottlenecks that arise when attempting to numerically integrate over long time periods sequentially, causing them to become computationally intractable in real time. By distributing a calculation across the many processors present in modern supercomputers, the computational load can be reduced drastically. Whilst spatially-parallel integration methods have been well explored in the literature, much less attention has been devoted to parallelisation in the time dimension.The aims and objectives of the research - The purpose of this PhD project will be to develop new (or improve existing) time-parallel integration algorithms, using stochastic and statistical methods, in order to reduce simulation times for large-scale systems of differential equations. The interplay between numerics and statistics (known as uncertainty quantification) is currently a very open field and the algorithm(s) being developed will need to be general enough to adapt to the complexity of the problems being solved.The novelty of the research methodology - The majority of currently known time-parallel algorithms have been formulated, studied and analysed using deterministic methods. The algorithm(s) developed in this project will incorporate a measure of stochasticity in order to exploit the statistical differences between deterministically generated solutions. In doing this, statistical and machine learning approaches may be exploited for numerical gain.The potential impact, applications, and benefits - A successfully designed algorithm could be used by UKAEA in order to significantly reduce simulation run times and hence integrate over previously (computationally) intractable ranges of time for magnetic fusion plasmas. These methods are not strictly limited to numerical fusion problems either. The same benefits could be realised in applications to other large-scale integration problems in climate modelling, astrophysics, drug research and many more.How the research relates to the remit - By developing statistically-based time-parallel algorithms with applications to magnetic fusion plasma, the proposed area of research contributes to multiple themes under the EPSRC remit. Namely the 'Numerical analysis' and 'UK Magnetic Fusion Research Programme' themes.Research area; Energy, Mathematical SciencesExternal Partner - Culham Centre for Fusion Energy (part of the UK Atomic Energy Authority)

研究背景-在许多科学分支中，从天体物理学到流行病学，数学和计算建模至关重要，通常涉及大型微分方程系统的数值积分。许多模拟受到瓶颈的限制，当试图在长时间内连续地进行数值积分时，会出现瓶颈，导致它们在真实的时间内变得难以计算。通过将计算分布在现代超级计算机中的许多处理器上，可以大大减少计算负荷。虽然空间并行积分方法已在文献中进行了很好的探讨，少得多的注意力一直致力于在时间dimension.The目的和研究目标的并行化-这个博士项目的目的将是开发新的（或改进现有的）时间并行积分算法，使用随机和统计方法，以减少模拟时间为大规模系统的微分方程。数值和统计之间的相互作用（称为不确定性量化）目前是一个非常开放的领域，正在开发的算法需要足够通用，以适应所解决问题的复杂性。研究方法的新奇-大多数目前已知的时间并行算法已经制定，研究和分析使用确定性方法。在这个项目中开发的算法（S）将纳入随机性的措施，以利用确定性生成的解决方案之间的统计差异。潜在的影响、应用和好处--UKAEA可以使用一个成功设计的算法来显著减少模拟运行时间，从而在磁聚变等离子体的以前（计算上）难以处理的时间范围内进行积分。这些方法也不严格限于数值融合问题。同样的好处可以实现在气候建模，天体物理学，药物研究和更多的其他大规模集成问题的应用程序。研究如何涉及的职权范围-通过开发与应用程序磁融合等离子体的基于时间的并行算法，研究的建议领域有助于多个主题下的EPSRC职权范围。即“数值分析”和“英国磁聚变研究计划”的主题。研究领域;能源，数学科学外部合作伙伴-卡勒姆聚变能中心（英国原子能管理局的一部分）