Interpretable Polynomial Neural Ordinary Differential Equations

• URL: http://arxiv.org/abs/2208.05072v1
• Date: Tue, 9 Aug 2022 23:23:37 GMT
• Title: Interpretable Polynomial Neural Ordinary Differential Equations
• Authors: Colby Fronk and Linda Petzold
• Abstract summary: We introduce the neural ODE, which is a deep neural network inside of the neural ODE framework. We demonstrate the capability of neural ODEs to predict outside of the training region, as well as perform direct symbolic regression without additional tools such as SINDy.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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