论文标题
可解释的多项式神经普通微分方程
Interpretable Polynomial Neural Ordinary Differential Equations
论文作者
论文摘要
神经网络具有充当通用函数近似器的能力，但它们不可解释，并且在其训练区域之外也不能概括。在尝试将标准神经普通微分方程（神经ODE）应用于动态系统时，这两个问题都是有问题的。我们介绍了多项式神经ODE，这是神经ode框架内部的深层神经网络。我们证明了多项式神经ODE的能力，可以预测训练区域外部，并在没有其他工具（例如Sindy）的情况下进行直接符号回归。
Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard neural ordinary differential equations (neural ODEs) to dynamical systems. We introduce the polynomial neural ODE, which is a deep polynomial neural network inside of the neural ODE framework. We demonstrate the capability of polynomial neural ODEs to predict outside of the training region, as well as perform direct symbolic regression without additional tools such as SINDy.
