论文标题
物理知识的神经网络，用于建模端口通道
A Physics-Informed Neural Network to Model Port Channels
论文作者
论文摘要
我们描述了一个物理信息的神经网络（PINN），该神经网络模拟了合成端口通道中天文潮流引起的流动，其尺寸基于Santos -SãoVicente -Bertioga estuarine系统。 Pinn模型旨在结合物理系统和数据驱动的机器学习模型的知识。这是通过训练神经网络来最大程度地减少样品中控制方程的残差来完成的。在这项工作中，我们的流程受近似值的Navier-Stokes方程的控制。本文有两个主要的新颖性。首先，我们设计模型以假设流动是周期性的，这在常规仿真方法中是不可行的。其次，我们评估了在训练过程中重新采样功能评估点的好处，该功能评估点的计算成本接近零，并已经过验证以改善最终模型，尤其是对于小批量尺寸。最后，我们讨论了有关湍流建模及其与PINN的相互作用的纳维尔 - 斯托克斯方程中使用的近似值的一些局限性。
We describe a Physics-Informed Neural Network (PINN) that simulates the flow induced by the astronomical tide in a synthetic port channel, with dimensions based on the Santos - São Vicente - Bertioga Estuarine System. PINN models aim to combine the knowledge of physical systems and data-driven machine learning models. This is done by training a neural network to minimize the residuals of the governing equations in sample points. In this work, our flow is governed by the Navier-Stokes equations with some approximations. There are two main novelties in this paper. First, we design our model to assume that the flow is periodic in time, which is not feasible in conventional simulation methods. Second, we evaluate the benefit of resampling the function evaluation points during training, which has a near zero computational cost and has been verified to improve the final model, especially for small batch sizes. Finally, we discuss some limitations of the approximations used in the Navier-Stokes equations regarding the modeling of turbulence and how it interacts with PINNs.
