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- W2885199841 abstract "The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced model. In this work, we explore a natural analogy between recurrent neural networks and the Mori-Zwanzig formalism to establish a systematic approach for developing reduced models with memory. Two training models-a direct training model and a dynamically coupled training model-are proposed and compared. We apply these methods to the Kuramoto-Sivashinsky equation and the Navier-Stokes equation. Numerical experiments show that the proposed method can produce reduced model with good performance on both short-term prediction and long-term statistical properties." @default.
- W2885199841 created "2018-08-22" @default.
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- W2885199841 date "2018-08-10" @default.
- W2885199841 modified "2023-10-14" @default.
- W2885199841 title "Model Reduction with Memory and the Machine Learning of Dynamical Systems" @default.
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- W2885199841 doi "https://doi.org/10.48550/arxiv.1808.04258" @default.
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