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).
Abstract (translated)
最近引入的类称为神经操作符的架构已经被证明是一种非常具有多才多艺的工具，适用于科学机器学习（SciML）领域的大多数任务，包括数据表示和预测。在这项研究中，我们研究了神经隐含流（NIF）作为一种新近开发的网格无关神经操作符，在表示库姆托夫-西弗辛格（KS）、强制库尔特韦格-德弗里斯（fKdV）和正弦- Gordon（SG）等规范系统的潜在动力学方面的能力，以及从它们中提取动态相关信息的能力。最后，我们评估了NIF作为维度降维算法的适用性，并对其与另一个被广泛认可的神经操作符家族——深度操作网络（DeepONets）进行了比较分析。
URL
https://arxiv.org/abs/2404.17535
