Physic-Informed Neural Network Approach Coupled with Boundary Conditions for Solving 1D Steady Shallow Water Equations for Riverine System
Physic-Informed Neural Network Approach Coupled with Boundary Conditions for Solving 1D Steady Shallow Water Equations for Riverine System
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DOI：
10.1061/9780784484852.027
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Ze-gao Yin;Linglong Bian;Beichao Hu;Jimeng Shi;Arturo S. Leon
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作者：
Ze-gao Yin;Linglong Bian;Beichao Hu;Jimeng Shi;Arturo S. Leon
浅水方程是明渠水流的控制方程。在过去的几十年中，数值解被广泛认为是求解SWE的最有效的方法。然而，数值解是低效的，并且需要在许多方面进行妥协，例如格式精度的阶数、Courant数、有界性等。近年来，深度学习（DL）一直是迅速崛起的技术之一，在工程领域得到了广泛的应用。DL模型可以通过人工神经网络构造的多个基本运算来桥接输入和输出变量之间的近似关系。许多研究者利用DL模型在水文和水力学问题上取得了成功。然而，仍然有一些缺点，以前的DL模型。这些DL模型通常是纯经验的，并且不受真实的物理的约束，这可能在训练数据集中不包括测试条件时导致更大的预测误差。此外，训练这个模型需要大数据，而大数据在水文和水力问题中通常是昂贵的。在本文中，我们将介绍一种新的和无数据的神经网络框架，可以解决SWE。该框架的体系结构将被详细演示，该框架可以应用于任何SWE问题。此外，我们采用了一个数值求解器，HEC-RAS，作为参考，以验证解决方案的准确性。结果表明，该框架与数值解非常吻合。
Shallow water equations (SWE) are the governing equations for the open channel flow. The numerical solution is widely considered the most effective approach for solving the SWE in the past few decades. However, numerical solutions are inefficient and need to compromise many aspects, such as order of scheme accuracy, Courant numbers, boundness, etc. In recent years, deep learning (DL) has been one of the rapidly rising techniques that have been widely used in the engineering field. DL models can bridge approximation relations between input and output variables by conducting multiple elementary operations constructed by artificial neural networks. Many researchers achieved success in hydrology and hydraulic problems by using DL models. However, there are still some drawbacks to the previous DL models. These DL models are often purely empirical and not constrained by real physics, which may cause a larger prediction error when test conditions are not included in the training data set. Besides, training this model requires big data, which is mostly expensive in hydrology and hydraulic problems. In this paper, we will introduce a novel and data-free neural network framework that can solve the SWE. The architecture of the framework will be demonstrated in detail, and the framework can be applied to any SWE problems. Additionally, we employed a numerical solver, HEC-RAS, as reference to verify the solution accuracy. As a result, this framework shows great agreement with numerical solutions.