论文标题
深欧方法：通过近似Euler方法的局部截断误差来求解ODE
Deep Euler method: solving ODEs by approximating the local truncation error of the Euler method
论文作者
论文摘要
在本文中，我们提出了一种基于深度学习的方法，深度Euler方法（DEM）来求解普通的微分方程。 DEM通过使用深神经网络近似局部截断误差来显着提高Euler方法的准确性，而深层神经网络可以获得具有较大步骤尺寸的高精度解决方案。 DEM中的深神经网络在训练过程中是无网状的，并且在未衡量的区域显示出良好的概括。 DEM可以很容易地与其他数值方法方案相结合，例如runge-kutta方法获得更好的解决方案。此外，讨论了DEM的误差和稳定性。
In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep neural networks which could obtain a high precision solution with a large step size. The deep neural network in DEM is mesh-free during training and shows good generalization in unmeasured regions. DEM could be easily combined with other schemes of numerical methods, such as Runge-Kutta method to obtain better solutions. Furthermore, the error bound and stability of DEM is discussed.
