Interpretable polynomial neural ordinary differential equations

Area of Science:

• Dynamical Systems and Machine Learning
• Artificial Intelligence
• Computational Mathematics

Background:

• Standard neural ordinary differential equations (ODEs) face challenges in interpretability and generalization.
• These limitations hinder their application in modeling complex dynamical systems.
• Existing methods often require additional tools for tasks like symbolic regression.

Purpose of the Study:

• To introduce a novel neural ODE framework that addresses interpretability and generalization issues.
• To develop a method for direct symbolic regression using neural networks.
• To improve the applicability of neural ODEs in scientific modeling.

Main Methods:

• Implementation of a deep polynomial neural network within the neural ODE framework.
• Development of the polynomial neural ODE model.
• Testing the model's performance on prediction tasks and symbolic regression.

Main Results:

• Polynomial neural ODEs demonstrate improved generalization capabilities, predicting accurately outside the training region.
• The model performs direct symbolic regression without relying on external algorithms like SINDy.
• Enhanced interpretability of the dynamical system models.

Conclusions:

• Polynomial neural ODEs offer a promising advancement for modeling dynamical systems.
• The framework enhances both the predictive accuracy and interpretability of neural ODEs.
• This approach simplifies the process of symbolic regression in scientific machine learning.