Interpretable Polynomial Neural Ordinary Differential Equations

Abstract

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.

References in corpus (4)

• PySINDy: A comprehensive Python package for robust sparse system identification
• Why Deep Neural Networks for Function Approximation?
• Sparse Identification for Nonlinear Optical Communication Systems: SINO Method
• Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling

Cited by in corpus (4)

• Symbolic Regression via Neural Networks
• Control of dynamical systems with neural networks
• Reconstructing Noisy Gene Regulation Dynamics Using Extrinsic-Noise-Driven Neural Stochastic Differential Equations
• Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcations