Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling Article Swipe

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Yonggi Park , Kelum Gajamannage , Dilhani I. Jayathilake , Erik M. Bollt ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2202.07022

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development and implementation of linear methods are relatively simple, but they often do not capture non-linear relationships in the data. Thus, artificial neural networks (ANNs) are receiving attention from researchers in analyzing and forecasting dynamical systems. Recurrent neural networks (RNN), derived from feed-forward ANNs, use internal memory to process variable-length sequences of inputs. This allows RNNs to applicable for finding solutions for a vast variety of problems in spatiotemporal dynamical systems. Thus, in this paper, we utilize RNNs to treat some specific issues associated with dynamical systems. Specifically, we analyze the performance of RNNs applied to three tasks: reconstruction of correct Lorenz solutions for a system with a formulation error, reconstruction of corrupted collective motion trajectories, and forecasting of streamflow time series possessing spikes, representing three fields, namely, ordinary differential equations, collective motion, and hydrological modeling, respectively. We train and test RNNs uniquely in each task to demonstrate the broad applicability of RNNs in reconstruction and forecasting the dynamics of dynamical systems.

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Recurrent Neural Network

Computer Science

Artificial Intelligence

Differential Equation

Mathematics

Physics

Quantum Mechanics

Mathematical Analysis

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Dynamical systems theory Recurrent neural network Computer science Autoregressive model Ordinary differential equation Artificial neural network Dynamical system (definition) Linear dynamical system Artificial intelligence Differential equation Mathematics Physics Quantum mechanics Econometrics Mathematical analysis

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2202.07022
PDF: https://arxiv.org/pdf/2202.07022
OA Status: green
Cited By: 2
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2202.07022

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Title: Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling

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Type: preprint

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Language: en

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Publication year: 2022

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Publication date: 2022-02-14

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Authors: Yonggi Park, Kelum Gajamannage, Dilhani I. Jayathilake, Erik M. Bollt

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Landing page: https://arxiv.org/abs/2202.07022

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PDF URL: https://arxiv.org/pdf/2202.07022

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Concepts: Dynamical systems theory, Recurrent neural network, Computer science, Autoregressive model, Ordinary differential equation, Artificial neural network, Dynamical system (definition), Linear dynamical system, Artificial intelligence, Differential equation, Mathematics, Physics, Quantum mechanics, Econometrics, Mathematical analysis

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Cited by: 2

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