  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.

Machine Learning