Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting

Traditional machine-learning methods are inefficient in capturing chaos in nonlinear dynamical systems, especially when the time difference <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</m...

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Autores principales:	Xiangyi Meng, Tong Yang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	quantum entanglement recurrent neural networks tensorization chaotic dynamical system chaotic time series forecasting Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/3992829212424edfbac8e23f66a783d5
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spelling	oai:doaj.org-article:3992829212424edfbac8e23f66a783d52021-11-25T17:30:07ZEntanglement-Structured LSTM Boosts Chaotic Time Series Forecasting10.3390/e231114911099-4300https://doaj.org/article/3992829212424edfbac8e23f66a783d52021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1491https://doaj.org/toc/1099-4300Traditional machine-learning methods are inefficient in capturing chaos in nonlinear dynamical systems, especially when the time difference <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>t</mi></mrow></semantics></math></inline-formula> between consecutive steps is so large that the extracted time series looks apparently random. Here, we introduce a new long-short-term-memory (LSTM)-based recurrent architecture by tensorizing the cell-state-to-state propagation therein, maintaining the long-term memory feature of LSTM, while simultaneously enhancing the learning of short-term nonlinear complexity. We stress that the global minima of training can be most efficiently reached by our tensor structure where all nonlinear terms, up to some polynomial order, are treated explicitly and weighted equally. The efficiency and generality of our architecture are systematically investigated and tested through theoretical analysis and experimental examinations. In our design, we have explicitly used two different many-body entanglement structures—matrix product states (MPS) and the multiscale entanglement renormalization ansatz (MERA)—as physics-inspired tensor decomposition techniques, from which we find that MERA generally performs better than MPS, hence conjecturing that the learnability of chaos is determined not only by the number of free parameters but also the tensor complexity—recognized as how entanglement entropy scales with varying matricization of the tensor.Xiangyi MengTong YangMDPI AGarticlequantum entanglementrecurrent neural networkstensorizationchaotic dynamical systemchaotic time series forecastingScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1491, p 1491 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	quantum entanglement recurrent neural networks tensorization chaotic dynamical system chaotic time series forecasting Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	quantum entanglement recurrent neural networks tensorization chaotic dynamical system chaotic time series forecasting Science Q Astrophysics QB460-466 Physics QC1-999 Xiangyi Meng Tong Yang Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
description	Traditional machine-learning methods are inefficient in capturing chaos in nonlinear dynamical systems, especially when the time difference <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>t</mi></mrow></semantics></math></inline-formula> between consecutive steps is so large that the extracted time series looks apparently random. Here, we introduce a new long-short-term-memory (LSTM)-based recurrent architecture by tensorizing the cell-state-to-state propagation therein, maintaining the long-term memory feature of LSTM, while simultaneously enhancing the learning of short-term nonlinear complexity. We stress that the global minima of training can be most efficiently reached by our tensor structure where all nonlinear terms, up to some polynomial order, are treated explicitly and weighted equally. The efficiency and generality of our architecture are systematically investigated and tested through theoretical analysis and experimental examinations. In our design, we have explicitly used two different many-body entanglement structures—matrix product states (MPS) and the multiscale entanglement renormalization ansatz (MERA)—as physics-inspired tensor decomposition techniques, from which we find that MERA generally performs better than MPS, hence conjecturing that the learnability of chaos is determined not only by the number of free parameters but also the tensor complexity—recognized as how entanglement entropy scales with varying matricization of the tensor.
format	article
author	Xiangyi Meng Tong Yang
author_facet	Xiangyi Meng Tong Yang
author_sort	Xiangyi Meng
title	Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
title_short	Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
title_full	Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
title_fullStr	Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
title_full_unstemmed	Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting
title_sort	entanglement-structured lstm boosts chaotic time series forecasting
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3992829212424edfbac8e23f66a783d5
work_keys_str_mv	AT xiangyimeng entanglementstructuredlstmboostschaotictimeseriesforecasting AT tongyang entanglementstructuredlstmboostschaotictimeseriesforecasting
_version_	1718412277624864768

Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting

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