Extraction of Information from Scientific Simulations

数值模拟是现代科学过程的基石，相当大的费用和精力，无论是字面上的还是比喻上的，都被投入到模拟中。这个项目的两个目标是(1)缩短模拟时间，(2)在给定现有模拟(但不是其完整历史)的输出的情况下对数据提出新的问题，以避免运行新的模拟。为了缩短模拟时间，幼稚的方法会导致对某些变量的估计不太准确，这些变量既用于预测新材料的性质，也用于对照已知性质验证数值模型。这个程序研究的是没有这种精确度损失的超分辨率方法。第二个目标记录了来自模拟的适当的随机快照或“草图”。因为事先可能不知道哪些变量应该直接计算，所以这个程序开发了一些技术来使用草图来估计最初没有计算的变量。该技术被设计成“面向未来”的模拟，并给数据集第二次有用的机会，而不需要运行新的模拟。在这个项目中实现其中一个或两个目标将减少不必要的计算机模拟，节省能源并减少对环境的影响。该项目汇集了物理化学、高性能计算、优化、机器学习、数字信号处理和时间序列统计的思想。更具体地说，第一个目标是从缩短的模拟中估计频谱变量。缩短时间范围通常具有加宽光谱线的效果。在谱的适当假设下，调和分析的最新进展表明，通过求解半定规划，可以超分辨谱线。这些进展一直局限于信号处理应用，经过适当的修改，它们将对从模拟中进行的谱估计产生重大影响。该项目将开发有效的算法来解决这个问题，并展示它如何适应科学计算的情况，并在理论上进行扩展，以正确处理不确定性。第二个目标是压缩参数估计，这是最近才探索的，主要是在数字信号处理的背景下进行的。该项目将为给定的统计数据开发特定的估计器，并探索一种适用于广泛统计类别的一般方法。存储数据快照的方法将主要应用于太阳对流的磁流体动力学(MHD)模拟，由于太阳天气对宇宙射线和入射到地球上的光子的影响，太阳对流是一个非常重要的领域。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。

Numerical simulations are a cornerstone of the modern scientific process, and considerable expense and energy, both literally and figuratively, is put into simulations. The two objectives of this project are to (1) shorten simulation time, and (2) ask new questions of the data given the output of an existing simulation (but not its full history) in order to avoid running a new simulation. To shorten simulation time, a naive approach leads to less accurate estimates of certain variables that are used for both prediction of new material properties and for validation of numerical models against known properties. This program investigates super-resolution methods that do not suffer this loss of accuracy. The second objective records appropriate randomized snapshots or "sketches" from simulations. Because it may not be known in advance which variables should be directly calculated, this program develops techniques to use the sketches to estimate variables that were not originally calculated. The technique is designed to "future-proof" simulations, and gives datasets a second chance at being useful without requiring a new simulation to be run. Achieving either or both objectives in this project will lead to fewer unnecessary computer simulations, saving energy and reducing impact on the environment.This project brings together ideas from physical chemistry, high-performance computing, optimization, machine learning, digital signal processing, and time-series statistics. More specifically, the first objective is to estimate spectral variables from a shortened simulation. Shortening the time range usually has the effect of broadening the spectral lines. Under appropriate assumptions on the spectra, recent advances in harmonic analysis show that by solving a semi-definite program, one can super-resolve the spectral lines. These advances have been limited to signal-processing applications, and with appropriate modification, they will have a great impact on spectral estimation from simulations. The project will develop efficient algorithms to tackle this problem, as well as show how it can be adapted to the situation of scientific computing, and theoretically extended to correctly handle uncertainty. The second objective is compressive parameter estimation, which has only recently been explored and mainly in the context of digital signal processing. The project will develop particular estimators for given statistics, as well as explore a general approach to apply to a broad class of statistics. The approach for storing snapshots of data will be applied primarily to magnetohydrodynamic (MHD) simulations of solar convection, a field of great importance due to the effect of the sun's weather on cosmic rays and photons incident on Earth.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.