Interpretable Polynomial Neural Ordinary Differential Equations
This addresses interpretability and generalization issues in neural ODEs for dynamical systems, though it appears incremental as it builds on existing frameworks.
The paper tackles the lack of interpretability and poor generalization of standard neural ODEs in dynamical systems by introducing polynomial neural ODEs, which can predict outside the training region and perform symbolic regression without extra tools.
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.