Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems

Imran Nasim, Joaõ Lucas de Sousa Almeida
4/26/2024
cs.LGcs.AI

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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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Cite this paper

@article{nasim2024using,
  title  = {Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems},
  author = {Imran Nasim and Joaõ Lucas de Sousa Almeida},
  year   = {2024},
  eprint = {2404.17535},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.17535v1}
}

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