Eindhoven University of Technology, 5600, Eindhoven, MB, The Netherlands.
Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Eur Phys J E Soft Matter. 2023 Mar 6;46(3):10. doi: 10.1140/epje/s10189-023-00267-w.
In this work, we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data were generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.
在这项工作中，我们探索了使用深度学习方法从数据碰撞算子中学习格子玻尔兹曼方法的可能性。我们比较了神经网络（NN）碰撞算子的层次设计，并评估了所得到的 LBM 方法在再现几种典型流动的时间动力学方面的性能。在目前的研究中，作为解决学习问题的首次尝试，数据是由单个弛豫时间 BGK 算子生成的。我们证明了普通的神经网络结构的准确性非常有限。另一方面，通过嵌入物理性质，如守恒定律和对称性，可以将准确性提高几个数量级，并正确再现标准流体流动的短时间和长时间动力学。
