论文标题
使用物理信息的神经网络产生动荡状态
Generation of Turbulent States using Physics-Informed Neural Networks
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
When modelling turbulent flows, it is often the case that information on the forcing terms or the boundary conditions is either not available or overly complicated and expensive to implement. Instead, some flow features, such as the mean velocity profile or its statistical moments, may be accessible through experiments or observations. We present a method based on physics-informed neural networks to generate turbulent states subject to a set of given conditions. The physics-informed method ensures the final state approximates a valid flow. We show examples of different statistical conditions that can be used to prepare states, motivated by experimental and atmospheric problems. Lastly, we show two ways of scaling the resolution of the prepared states. One is through the use of multiple and parallel neural networks. The other uses nudging, a synchronization-based data assimilation technique that leverages the power of specialized numerical solvers.
