Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has imposed severe limitations on the amount of data that can be stored and has elevated the issue of input/output (I/O) into one of the major bottlenecks of high-performance computing. In this work, we present an in situ compression technique to reduce the size of the data storage by orders of magnitude. This methodology is based on time-dependent subspaces and it extracts low-rank structures from multidimensional streaming data by decomposing the data into a set of time-dependent bases and a core tensor. We derive closed-form evolution equations for the core tensor as well as the time-dependent bases. The presented methodology does not require the data history and the computational cost of its extractions scales linearly with the size of data — making it suitable for large-scale streaming datasets. To control the compression error, we present an adaptive strategy to add/remove modes to maintain the reconstruction error below a given threshold. We present four demonstration cases: (i) analytical example, (ii) incompressible unsteady reactive flow, (iii) stochastic turbulent reactive flow, and (iv) three-dimensional turbulent channel flow.

对时间相关问题的大规模模拟会产生大量数据，并且随着计算资源的爆炸式增长，这些模拟产生的数据量也显着增加。这对可存储的数据量施加了严重限制，并将输入/输出 (I/O) 问题提升为高性能计算的主要瓶颈之一。在这项工作中，我们提出了一个原位压缩技术可将数据存储的大小减少几个数量级。该方法基于时间相关的子空间，它通过将数据分解为一组时间相关的基和核心张量，从多维流数据中提取低秩结构。我们推导出核心张量和时间相关基的封闭式演化方程。所提出的方法不需要数据历史，其提取的计算成本与数据大小成线性关系——使其适用于大规模流数据集。为了控制压缩误差，我们提出了一种自适应策略来添加/删除模式，以将重建误差保持在给定阈值以下。我们提出了四个示范案例：（i）分析示例，（ii）不可压缩的非定常反应流，