Parallel-in-time computation for sedimentary landscapes

沉积景观的并行时间计算

• 批准号: EP/W015439/1
• 负责人: Colin Cotter
• 金额: $ 10.27万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW015439%2F1
• 关键词: Parallel; time; computation; sedimentary; landscapes

This proposal is about novel mathematical techniques underpinningcomputational stratigraphic models that simulate the formation oflandscapes of sedimentary rock. Sedimentary rocks form after gradualsettling of microscopic particles (formed from minerals, or comingfrom plants or animals) that are suspended in ocean water. Overmillions of years, the particles settle on the ocean floor, eventuallycondensing into rocks such as shale and limestone. By mathematicallymodelling this process on a computer and comparing with geologicaldata, we can learn about the evolution of our present landscape onPlanet Earth, and we can use it to fill in the gaps betweendata. These models have applications in locating carbon capture andstorage sites, and in reconstructions of recent geological history ofcoral reefs, for example.Stratigraphic models simulate the evolution of the sediment over time,stepping from one moment in time to a later one in the near future,executing "timesteps" one by one in a sequential manner. Accuratemodelling of the sediment processes requires that these timesteps are0.1-1 years long. Since sedimentary landscapes form over geologicaleras that are millions of years long, this means that we have toexecute millions of timesteps, one after the other. This isprohibitively long, especially when the models are needed for dataassimilation algorithms that search for unknown properties of pastrock formation processes in the light of data obtained from geologicalmeasurement campaigns. This is because these data assimilationalgorithms have to repeat the simulation many times with varyingparameter values. In these situations, stratigraphic modellers areforced to use timesteps that are 1000s of years long: this yieldsresults of insufficient accuracy.Our goal is to create new mathematical techniques that can make use ofhighly parallel supercomputers, leading to much faster simulations andenabling more sophisticated data assimilation algorithms to be used.Instead of the sequential one-timestep-at-a-time approach, we willcreate new algorithms that solve for all of the timestepssimultaneously on a large number of computer processors in parallel.We call this parallel-in-time integration. The algorithms will beiterative, computing first guesses for the model predictions for eachtimestep and then updating them until they are sufficientlyaccurate. A good parallel-in-time integration method will only requirea small number of iterations, so that the result of the algorithm isquicker than sequential computation. Finding a good parallel-in-timeintegration method is a mathematical problem, with the number ofiterations being strongly dependent on the structure of the equationsthat describe the simulation model. Parallel-in-time approaches havenever been investigated for stratigraphic models. In this project wewill start a new field of numerical analysis research, designingparallel-in-time integration methods for stratigraphic models andanalysing them using a blend of theoretical analysis and highperformance computational experiments to identify the best pathforward.

该提议是关于基础计算层层模型的新型数学技术，该技术模拟了沉积岩石景观的形成。在悬浮在海水中的微观颗粒（由矿物或动物的降临物形成）逐渐燃料（由矿物或降落的动物形成）后形成沉积岩。超过数百万年的颗粒落在海底上，最终构成了页岩和石灰石等岩石。通过在计算机上数学编码这一过程并与地质数据进行比较，我们可以了解当前景观OnPlanet Earth的演变，我们可以使用它来填补bapweendata的空白。这些模型在定位碳捕获和存储地点以及重建最近的地质历史上有应用。沉积物过程的准确销售要求这些时间步长为0.1 - 1年。由于在数百万年的地质上形成了沉积景观，因此这意味着我们必须执行数百万个时间段，一个接一个。这是长时间的，尤其是当需要根据地质计量活动获得的数据来搜索pastrock形成过程的未知属性的数据密集算法时。这是因为这些数据同化为以不同的参数值重复多次模拟。在这些情况下，地层模块被迫使用时间到1000年的时间步长：这将产生不足的准确性。我们的目标是创建新的数学技术，这些技术可以使高度平行的超级计算机可以使用更快的模拟和更典型的数据，从而实现了更加有成熟的数据，以实现更典型的数据，以实现序列，以实现良好的效果。方法，我们将创建新的算法，这些算法并行在大量计算机处理器上求解所有时间段。我们称此并行时间集成。这些算法将良好，计算每个三键预测的模型预测，然后对其进行更新，直到它们充分使用为止。良好的平行时间集成方法只需要少量的迭代，因此算法ISQuicker的结果比顺序计算。找到一个良好的平行时间整合方法是一个数学问题，其中的数量很大程度上取决于方程的结构，这些方程描述了仿真模型。研究地层模型已研究并行的方法。在这个项目中，我们将开始一个新的数值分析研究领域，使用理论分析和高性能计算实验的融合，为地层模型设计了时间的积分方法，并将其设计为识别最佳路径。