论文标题
对物理知识深度学习的实验设计的最新评论
State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning
论文作者
论文摘要
本文对替代模型中使用的实验的设计进行了全面综述。特别是，这项研究证明了属于监督学习类别的物理信息神经网络（PINN）的实验方案设计的必要性。许多复杂的部分微分方程（PDE）没有任何分析解决方案。仅使用数值方法来求解计算昂贵的方程式。近几十年来，Pinn已获得流行，以替代减少计算预算的数值方法。 Pinn使用微分方程形式的物理信息来增强神经网络的性能。尽管它有效地工作，但实验方案的设计选择很重要，因为使用PINN的预测响应的准确性取决于训练数据。在这项研究中，将五个不同的PDE用于数值目的，即粘性汉堡方程，Shrödinger方程，热方程，Allen-Cahn方程和Korteweg-de Vries方程。进行了比较研究以确定选择DOE方案的必要性。可以看出，基于Hammersley采样的PINN的性能比其他DOE样本策略更好。
This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN), which belongs to the supervised learning class. Many complex partial differential equations (PDEs) do not have any analytical solution; only numerical methods are used to solve the equations, which is computationally expensive. In recent decades, PINN has gained popularity as a replacement for numerical methods to reduce the computational budget. PINN uses physical information in the form of differential equations to enhance the performance of the neural networks. Though it works efficiently, the choice of the design of experiment scheme is important as the accuracy of the predicted responses using PINN depends on the training data. In this study, five different PDEs are used for numerical purposes, i.e., viscous Burger's equation, Shrödinger equation, heat equation, Allen-Cahn equation, and Korteweg-de Vries equation. A comparative study is performed to establish the necessity of the selection of a DoE scheme. It is seen that the Hammersley sampling-based PINN performs better than other DoE sample strategies.
