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

Park, Yonggi; Gajamannage, Kelum; Jayathilake, Dilhani Ishanka; Bollt, Erik M.

doi:10.48550/arxiv.2202.07022

Cited by 3 publications

(2 citation statements)

References 29 publications

(53 reference statements)

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“…Our analysis has so far has made the rather ideal assumption that the observations are unperturbed by any noise. Reservoir computers appear to be fairly resilient to noise in time series forecasting problems [26], which suggests that under noisy observations an (injective) GS is preserved in some form. With this inspiration we will assume that the observations are perturbed by Gaussian white noise with an amplitude σ ∈ C 0 (M, R + ).…”

Section: Generalised Synchronisations With Noisy Observationsmentioning

confidence: 99%

Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers

Hart

2022

SSRN Journal

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Section: Generalised Synchronisations With Noisy Observationsmentioning

confidence: 99%

Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers

Hart

2022

SSRN Journal

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“…Recurrent Neural Networks (RNNs) are powerful and robust types of ANNs that belong to the most promising algorithms in use because of their internal memory (Park et al, 2022). This internal memory remembers its inputs and helps RNN to find solutions for a vast variety of problems (Ma & Principe, 2018).…”

Section: Introductionmentioning

confidence: 99%

Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Many-to-one LSTMs

Gajamannage¹,

Park²

2022

Preprint

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Financial markets are highly complex and volatile; thus, learning about such markets for the sake of making predictions is vital to make early alerts about crashes and subsequent recoveries. People have been using learning tools from diverse fields such as financial mathematics and machine learning in the attempt of making trustworthy predictions on such markets. However, the accuracy of such techniques had not been adequate until artificial neural network (ANN) frameworks were developed. Moreover, making accurate realtime predictions of financial time series is highly subjective to the ANN architecture in use and the procedure of training it. Long short-term memory (LSTM) is a member of the recurrent neural network family which has been widely utilized for time series predictions. Especially, we train two LSTMs with a known length, say T time steps, of previous data and predict only one time step ahead. At each iteration, while one LSTM is employed to find the best number of epochs, the second LSTM is trained only for the best number of epochs to make predictions. We treat the current prediction as in the training set for the next prediction and train the same LSTM. While classic ways of training result in more error when the predictions are made further away in the test period, our approach is capable of maintaining a superior accuracy as training increases when it proceeds through the testing period. The forecasting accuracy of our approach is validated using three time series from each of the three diverse financial markets: stock, cryptocurrency, and commodity. The results are compared with those of an extended Kalman filter, an autoregressive model, and an autoregressive integrated moving average model.

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A review on big data based on deep neural network approaches

Rithani,

Kumar,

Doss

2023

Artif Intell Rev

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

Cited by 3 publications

References 29 publications

Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers

Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers

Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Many-to-one LSTMs

A review on big data based on deep neural network approaches

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