Fourier-RNNs for Modelling Noisy Physics Data

TL;DR

This paper introduces Fourier-RNNs, a novel sequential model combining RNNs with Fourier Neural Operators, designed to effectively model noisy, non-Markovian physics data, outperforming traditional models in such scenarios.

Contribution

The paper proposes a new Fourier-RNN architecture that integrates Fourier Neural Operators with RNNs to better handle noisy and non-Markovian physics data.

Findings

Fourier-RNN performs as well as FNO on PDE data.

Fourier-RNN outperforms FNO and RNN on noisy, non-Markovian data.

The model effectively captures complex temporal dependencies in physics data.

Abstract

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.