Using Neural Implicit Flow to represent latent dynamics of canonical systems

Abstract

The recently introduced class of architectures known as Neural Operators has emerged as highly versatile tools applicable to a wide range of tasks in the field of Scientific Machine Learning (SciML), including data representation and forecasting. In this study, we investigate the capabilities of Neural Implicit Flow (NIF), a recently developed mesh-agnostic neural operator, to represent the latent dynamics of canonical systems such as the Kuramoto-Sivashinsky (KS) and forced Korteweg–de Vries (fKdV) equations and to extract dynamically relevant information from them. Finally we assess the applicability of NIF as a dimensionality reduction algorithm and conduct a comparative analysis with another widely recognized family of neural operators, known as Deep Operator Networks (DeepONets).