Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems

2024/04/26 by Imran Nasim, Nasim, Imran, João Lucas de Sousa Almeida +1 · 1 citation
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2404.17535

openalex publication_date 2024/04/26 · openalex created_date 2024/04/30 · openalex updated_date 2026/07/28

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).

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