Interpretable Polynomial Neural ODEs

May 2, 2025

TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Linda Petzold, UC Santa Barbara, Mechanical Engineering and Computer Science

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.   Stiffness (the presence of multiple time scales, the fastest of which are stable) has been a challenge for neural ODEs. We show how to address this issue using single-step implicit methods or the (explicit) integrating factor Euler method.

HOST: Efstathios Charalampidis

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