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Journal of Machine Learning for Modeling and Computing

Publicado 4 números por año

ISSN Imprimir: 2689-3967

ISSN En Línea: 2689-3975

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LEARNING REDUCED SYSTEMS VIA DEEP NEURAL NETWORKS WITH MEMORY

Volumen 1, Edición 2, 2020, pp. 97-118
DOI: 10.1615/.2020034232
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SINOPSIS

We present a general numerical approach for constructing governing equations for unknown dynamical systems when data on only a subset of the state variables are available. The unknown equations for these observed variables are thus a reduced system of the complete set of state variables. Reduced systems possess memory integrals, based on the well-known Mori-Zwanzig (MZ) formulation. Our numerical strategy to recover the reduced system starts by formulating a discrete approximation of the memory integral in the MZ formulation. The resulting unknown approximate MZ equations are of finite dimensional, in the sense that a finite number of past history data are involved. We then present a deep neural network structure that directly incorporates the history terms to produce memory in the network. The approach is suitable for any practical systems with finite memory length. We then use a set of numerical examples to demonstrate the effectiveness of our method.

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CITADO POR
  1. Qin Tong, Chen Zhen, Jakeman John D., Xiu Dongbin, Data-Driven Learning of Nonautonomous Systems, SIAM Journal on Scientific Computing, 43, 3, 2021. Crossref

  2. Chen Zhen, Churchill Victor, Wu Kailiang, Xiu Dongbin, Deep neural network modeling of unknown partial differential equations in nodal space, Journal of Computational Physics, 449, 2022. Crossref

  3. Chekroun Mickaël D., Liu Honghu, McWilliams James C., Stochastic rectification of fast oscillations on slow manifold closures, Proceedings of the National Academy of Sciences, 118, 48, 2021. Crossref

  4. Fu Xiaohan, Mao WeiZe , Chang Lo-Bin, Xiu Dongbin, MODELING UNKNOWN DYNAMICAL SYSTEMS WITH HIDDEN PARAMETERS , Journal of Machine Learning for Modeling and Computing, 3, 3, 2022. Crossref

  5. Churchill Victor, Xiu Dongbin, LEARNING FINE SCALE DYNAMICS FROM COARSE OBSERVATIONS VIA INNER RECURRENCE, Journal of Machine Learning for Modeling and Computing, 3, 3, 2022. Crossref

  6. Jones Reese E., Frankel Ari L., Johnson K. L. , A NEURAL ORDINARY DIFFERENTIAL EQUATION FRAMEWORK FOR MODELING INELASTIC STRESS RESPONSE VIA INTERNAL STATE VARIABLES , Journal of Machine Learning for Modeling and Computing, 3, 3, 2022. Crossref

  7. Churchill Victor, Xiu Dongbin, DEEP LEARNING OF CHAOTIC SYSTEMS FROM PARTIALLY-OBSERVED DATA , Journal of Machine Learning for Modeling and Computing, 3, 3, 2022. Crossref

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