Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems

TL;DR

This paper explores Neural Implicit Flow (NIF), a mesh-agnostic neural operator, for modeling latent dynamics of canonical systems and compares its effectiveness with DeepONets in scientific machine learning tasks.

Contribution

It demonstrates NIF's capability to represent complex system dynamics and evaluates its performance against existing neural operators like DeepONets.

Findings

NIF effectively models latent dynamics of canonical systems.

NIF outperforms or matches DeepONets in key tasks.

NIF shows promise as a dimensionality reduction tool.

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, 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).