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).
Cite
@article{arxiv.2404.17535,
title = {Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems},
author = {Imran Nasim and Joaõ Lucas de Sousa Almeida},
journal= {arXiv preprint arXiv:2404.17535},
year = {2024}
}
Comments
Accepted into the International conference on Scientific Computation and Machine Learning 2024 (SCML 2024)