Tucker Decomposition for Interpretable Neural Ordinary Differential Equations

Abstract

Tensorial and polynomial networks have emerged as effective tools in vari- ous fields, particularly for modeling the multilinear relationships among input variables. More recently, polynomial networks factorized using the canonical polyadic tensor decomposition (CPD) have been successfully used in the prob- lem of system dynamics identification, where the relations between variables are usually a polynomial function. This paper introduces a more general tensorial net- work that employs Tucker decomposition, thereby providing enhanced flexibility and expressivity in model construction. The study evaluates the performance of TuckerNet, comparing it against CPD-based networks in learning functions and identifying ordinary differential equation dynamics. The findings demonstrate the potential of TuckerNet as a superior alternative for tensorial network construction, particularly when constraining the number of parameters, while also highlighting aspects beyond decomposition that impact learning outcomes.