Fourier-RNNs for Modelling Noisy Physics Data
This work addresses the challenge of handling noisy physics data for researchers in computational physics and machine learning, representing an incremental improvement by hybridizing existing methods.
The authors tackled the problem of modelling noisy physics data by proposing Fourier-RNN, a sequential model that combines RNNs with Fourier Neural Operators, which outperforms FNO and conventional RNNs on noisy, non-Markovian data.
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.