Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain computationally expensive: In this paper, we resort to the theory of modified equations in order to obtain ''on the fly'' cheap numerical approximations. The recipe consists in approximating, prior to that, the modified field associated to the modified equation by neural networks. Elementary convergence results are then established and the efficiency of the technique is demonstrated on experiments.

翻译：普通微分方程通常难以得到解析解。一般使用通用数值化方法求近似解，但精确的计算方法十分耗时。本文采用改进方程理论，以得到实时的低成本数值计算。具体方法为，在求解之前，利用神经网络对修改方程对应的修改场进行逼近。文章证明了基本收敛结果，并使用实验数据展示了这种技术的高效性。