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Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

arXiv 1802.07486 ↗First posted 21 Feb 2018physics.comp-ph cs.LG nlin.CDcited by 155

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Abstract (arXiv)

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

Key facts. Cited by 155 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Feb 2018.

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Citing papers per year: 2021: 33; 2022: 33; 2023: 23; 2024: 21; 2025: 20; 2026: 25.

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38 more
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  5. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 29
  6. 2021Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equationscited by 28
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  11. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
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  15. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 18
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  18. 2024Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observationscited by 16
  19. 2021Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformerscited by 15
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  21. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
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  26. 2022W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecastingcited by 12
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  28. 2023Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecastscited by 11
  29. 2022Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order modelscited by 10
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  35. 2024A non-intrusive machine learning framework for debiasing long-time coarse resolution climate simulations and quantifying rare events statisticscited by 9
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  37. 2021Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operatorscited by 8
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50 most cited of 155 All 155 (JSON)