论文标题
反向修改的微分方程，以发现动力学
Inverse modified differential equations for discovery of dynamics
论文作者
论文摘要
数值集成与深度学习（即ode-net）的结合已成功地用于各种应用中。在这项工作中，我们引入了反修改的微分方程（IMDE），以促进使用ODE-NET发现动力学发现动态的行为和误差分析。结果表明，学到的ode和截断的IMDE之间的差异受学习损失的总和和差异的限制，而差异可以呈指数为小。此外，我们推断出ODE-NET的总误差是由离散误差和学习损失的总和。此外，在IMDE的帮助下，得出了学习哈密顿系统的理论结果。进行了几项实验以在数值上验证我们的理论结果。
The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour and error analysis of discovery of dynamics using ODE-net. It is shown that the difference between the learned ODE and the truncated IMDE is bounded by the sum of learning loss and a discrepancy which can be made sub exponentially small. In addition, we deduce that the total error of ODE-net is bounded by the sum of discrete error and learning loss. Furthermore, with the help of IMDE, theoretical results on learning Hamiltonian system are derived. Several experiments are performed to numerically verify our theoretical results.
