Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems

• URL: http://arxiv.org/abs/2404.17535v1
• Date: Fri, 26 Apr 2024 17:01:38 GMT
• Title: Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems
• Authors: Imran Nasim, Joaõ Lucas de Sousa Almeida,
• Abstract summary: We present the capabilities of Neural Implicit Flow (NIF), a recently developed mesh-agnostic neural operator. NIF represents the latent dynamics of canonical systems such as the Kuramoto-Sivashinsky (KS), forced Korteweg-de Vries (fKdV), and Sine-Gordon (SG) equations. We also conduct a comparative analysis with another widely recognized family of neural operators, known as Deep Operator Networks (DeepONets)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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