Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems
<|reference_start|>Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems: 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).<|reference_end|>
@article{nasim2024using,
    title={Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical
  Systems},
    author={Imran Nasim, Joa~o Lucas de Sousa Almeida},
    journal={arXiv preprint arXiv:2404.17535},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17535},
    primaryClass={cs.LG cs.AI}
}