论文标题
部分可观测时空混沌系统的无模型预测
Physics-informed data based neural networks for two-dimensional turbulence
论文作者
论文摘要
湍流仍然是一个尚未完全理解的问题，实验性和数值研究旨在充分表征湍流的统计特性。这样的研究需要大量资源来捕获，模拟，存储和分析数据。在这项工作中，我们提出了基于物理信息的神经网络（PINN）方法，以借助具有周期性界限的矩形域中的稀疏数据来预测二维湍流的流量和特征。尽管Pinn模型可以在大规模上重现所有统计数据，但小规模的性质未正确捕获。我们引入了一种新的Pinn模型，该模型可以有效地捕获小尺度上的能量分布，其性能比基于标准的PINN方法更好。它依赖于对低波数和高波数行为的训练，从而可以更好地估计全部湍流。使用0.1％的训练数据，我们观察到，与直接数值模拟（DNS）的解决方案相比，新的Pinn模型在惯性尺度上捕获了惯性尺度的湍流场。我们进一步应用这些技术来成功捕获湍流中大规模模式的统计行为。我们认为，在更短的时间间隔内增强现有湍流数据集的检索时，具有重要的应用程序。
Turbulence remains a problem that is yet to be fully understood, with experimental and numerical studies aiming to fully characterise the statistical properties of turbulent flows. Such studies require huge amount of resources to capture, simulate, store and analyse the data. In this work, we present physics-informed neural network (PINN) based methods to predict flow quantities and features of two-dimensional turbulence with the help of sparse data in a rectangular domain with periodic boundaries. While the PINN model can reproduce all the statistics at large scales, the small scale properties are not captured properly. We introduce a new PINN model that can effectively capture the energy distribution at small scales performing better than the standard PINN based approach. It relies on the training of the low and high wavenumber behaviour separately leading to a better estimate of the full turbulent flow. With 0.1 % training data, we observe that the new PINN model captures the turbulent field at inertial scales leading to a general agreement of the kinetic energy spectra upto eight to nine decades as compared with the solutions from direct numerical simulation (DNS). We further apply these techniques to successfully capture the statistical behaviour of large scale modes in the turbulent flow. We believe such methods to have significant applications in enhancing the retrieval of existing turbulent data sets at even shorter time intervals.
