Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems
This work addresses the problem of modeling complex dynamical systems in scientific machine learning, but it is incremental as it builds on existing neural operator frameworks.
The study applied Neural Implicit Flow (NIF) to represent latent dynamics in canonical systems like Kuramoto-Sivashinsky and Sine-Gordon equations, and compared it with DeepONets for dimensionality reduction, showing its effectiveness as a mesh-agnostic neural operator.
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, for representing the latent dynamics of canonical systems such as the Kuramoto-Sivashinsky (KS), forced Korteweg-de Vries (fKdV), and Sine-Gordon (SG) equations, as well as for extracting 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).