Parallel-in-time computation for sedimentary landscapes

这个建议是关于新的数学技术，支持模拟沉积岩景观形成的计算地层模型。沉积岩是在悬浮在海水中的微观颗粒（由矿物形成，或来自植物或动物）逐渐沉降后形成的。数百万年后，这些微粒沉淀在海底，最终凝结成页岩和石灰岩等岩石。通过在计算机上模拟这一过程并与地质数据进行比较，我们可以了解地球上目前景观的演变，我们可以用它来填补数据之间的空白。这些模型可以应用于定位碳捕获和储存地点，以及重建珊瑚礁的近代地质历史。地层模型模拟沉积物随时间的演变，从一个时刻到不久的将来的一个时刻，以连续的方式一个接一个地执行“时间步”。沉积过程的精确模拟要求这些时间步长为0.1 -1年。由于沉积地貌是在数百万年的地质时代形成的，这意味着我们必须执行数百万个时间步长，一个接一个。这是令人望而却步的长，特别是当模型需要的数据同化算法，搜索未知属性的pastrock形成过程中的光从geologicalmeasurement活动获得的数据。这是因为这些数据同化算法必须用不同的参数值重复模拟多次。在这些情况下，地层建模者被迫使用长达1000年的时间步长：我们的目标是创造新的数学技术，可以利用高度并行的超级计算机，导致更快的模拟和使更复杂的数据同化算法被使用。而不是顺序的一次一步的方法，我们将创建新的算法，在大量的计算机处理器上并行地同时求解所有的时间步。我们称之为时间并行积分。算法将是迭代的，首先计算每个时间步的模型预测，然后更新它们，直到它们非常准确。一个好的时间并行积分方法只需要很少的迭代次数，因此算法的结果比顺序计算快。寻找一个好的时间并行积分方法是一个数学问题，迭代次数强烈依赖于描述仿真模型的方程的结构。地层模型的时间序列方法从未被研究过。在这个项目中，我们将开始一个新的数值分析研究领域，设计地层模型的时间并行积分方法，并使用理论分析和高性能计算实验的混合来分析它们，以确定最佳前进路径。

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.