Solving flows of dynamical systems by deep neural networks and a novel deep learning algorithm
Solving flows of dynamical systems by deep neural networks and a novel deep learning algorithm
复制标题
通过深度神经网络和新颖的深度学习算法解决动力系统的流动
DOI：
10.1016/j.matcom.2022.06.004
复制
发表时间：
2022-06
影响因子：
4.6
通讯作者：
Limin Zhang
中科院分区：
文献类型：
--
作者：
Guangyuan Liao;Limin Zhang
机器学习变得流行并用于解决应用科学各个领域的广泛问题。在动力系统中，机器学习方法用于求解微分方程。在本文中，我们开发了一个人工网络来求解常微分方程组。对于网络，我们使用多层感知器网络，它是一个全连接的前馈网络，用于预测特定系统的流量。为了改进该方法的长时间估计，我们引入了上限控制策略。为了处理刚性ODE系统(如慢-快耦合系统)，引入了一种新的算法——有限神经元法。通过数值模拟，证明该算法比直接机器学习方法具有更好的效率和准确性。 • 开发深度神经网络来求解微分方程的一组解。 • 引入神经网络控制策略以提高方法的准确性。 • 有限神经元方法能够求解具有多个时间尺度的系统。
Machine learning becomes popular and is used for a wide range of problems in various areas of applied sciences. In dynamical systems, machine learning methods are applied to solve differential equations. In this paper, we develop an artificial network to solve systems of ordinary differential equations. For the network, we use a multilayer perceptron networks, which is a fully connected feedforward network to predict the flow of a specific system. In order to improve the long time estimation of the method, we introduced an upper bound control strategy. To deal with stiff ODE systems(such as slow-fast coupled system), a new algorithm, Finite Neural Element method, is introduced. By numerical simulation, the novel algorithm is proved to have better efficiency and accuracy than direct machine learning method. • A deep neural network is developed to solve a bundle of solutions of the differential equations. • A control strategy for the neural network is introduced to increase the accuracy of the method. • The Finite Neural Element method is capable of solving systems with multiple time scales.
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DOI：
10.1016/j.cma.2019.112790
发表时间：
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影响因子：
7.2
作者：
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通讯作者：
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影响因子：
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