Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required temporal dependencies. However, most existing sequential models operate within finite-dimensional Euclidean spaces which offer limited functionality when employed in modelling physics relevant data. Alternatively recent work with neural operator learning within the Fourier space has shown efficient strategies for parameterising Partial Differential Equations (PDE). In this work, we propose a novel sequential model, built to handle Physics relevant data by way of amalgamating the conventional RNN architecture with that of the Fourier Neural Operators (FNO). The Fourier-RNN allows for learning the mappings from the input to the output as well as to the hidden state within the Fourier space associated with the temporal data. While the Fourier-RNN performs identical to the FNO when handling PDE data, it outperforms the FNO and the conventional RNN when deployed in modelling noisy, non-Markovian data.

翻译：经典时间序列预测中的序列模型依赖通过隐状态学习从过去到未来实例的映射。隐状态表征历史信息并编码所需的时间依赖性。然而，现有序列模型大多在有限维欧几里得空间中运行，这在建模物理相关数据时功能有限。近年来，傅里叶空间中的神经算子学习为参数化偏微分方程提供了高效策略。本研究提出一种新型序列模型，通过融合传统RNN架构与傅里叶神经算子来适配物理相关数据处理。傅里叶RNN能够在与时间数据关联的傅里叶空间中学习输入到输出以及输入到隐状态的映射。在处理偏微分方程数据时，傅里叶RNN性能与FNO相当；但在建模含噪非马尔可夫数据时，其表现优于FNO和传统RNN。