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).

翻译：最近引入的神经算子架构系列已成为科学机器学习领域（SciML）中高度通用的工具，适用于包括数据表示与预测在内的广泛任务。本研究探究了神经隐式流（NIF）——一种新开发的网格无关神经算子——在表征Kuramoto-Sivashinsky（KS）方程、受迫Korteweg-de Vries（fKdV）方程和Sine-Gordon（SG）方程等典型系统潜动力学方面的能力，以及从中提取动力学相关信息的能力。最后，我们评估了NIF作为降维算法的适用性，并与另一类广泛认可的神经算子——深度算子网络（DeepONets）进行了比较分析。