When Neural ODEs meet Neural Operators

Woojin Cho, Seunghyeon Cho, Hyundong Jin, Jinsung Jeon, Kookjin Lee, Sanghyun Hong, Dongeun Lee, Jonghyun Choi, Noseong Park

Abstract: Differential equation-based neural networks perform well in a variety of deep learning fields. Among those many methods, neural ordinary differential equations (NODEs) are one of the most fundamental work. NODEs have been applied to general downstream tasks such as image classification, time series classification, and image generation. The ODE function of NODEs can be understood as a special type of differential operators, which had been overlooked before. In this paper, therefore, we study the feasibility of modeling NODEs (or the ODE function of NODEs) as neural operators. Our neural operator-based methods are more rigorous than existing approaches when it comes to learning the differential operator (or the ODE function). To this end, we design a new neural operator structure called branched Fourier neural operator (BFNO), which is suitable for modeling the ODE function. It shows improved performance for several general machine learning tasks, as compared to existing various NODE models.

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