Interpretable polynomial neural ordinary differential equations

Colby Fronk; Linda Petzold

doi:10.1063/5.0130803

Interpretable polynomial neural ordinary differential equations

Chaos. 2023 Apr 1;33(4):043101. doi: 10.1063/5.0130803.

Authors

Colby Fronk¹, Linda Petzold^{2

3}

Affiliations

¹ Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA.
² Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA.
³ Department of Computer Science, University of California, Santa Barbara, California 93106, USA.

Abstract

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and do not generalize well outside of their training region. Both of these issues are problematic when trying to apply standard neural ordinary differential equations (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 to perform direct symbolic regression without using additional tools such as SINDy.

Grants and funding

R01 EB014877/EB/NIBIB NIH HHS/United States