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<p>The rapid expansion of machine learning has produced a wide range of data-driven methods that may be applied to unsteady fluid mechanics. The vast amount of options may overwhelm users in fluid mechanics when choosing the most suitable method for their problem. This work establishes user guidelines by investigating five widely used techniques: Dynamical Mode Decomposition with Control (DMDc), Sparse Identification of Nonlinear Dynamics (SINDy), Discrete Timestepping Multilayer Perceptron (MLP), State-Space Neural Network (SS-NN), and Long Short-Term Memory neural networks (LSTM). The methods are presented within a common state-space framework to highlight their similarities and differences. Their ability to produce accurate long-term predictions of wake variables for control implementation is evaluated via the high-dimensional, unsteady, and nonlinear fluid mechanics system of a flow past an oscillating cylinder. During the modelling process, practical recommendations are provided to help users enhance model performance. The main findings are as follows: DMDc offers a reliable, interpretable, and efficient linear baseline model. SINDy’s performance depends on careful selection of basis functions and is sensitive to coordinate space used to represent the dynamics; while powerful for low-complexity systems, it struggles with stability in complex dynamics. MLP are the simplest form of NN-based model but require multiple hidden layers leading to a strong impact of the parameter initialisation on the performance. SS-NN models require careful tuning of model complexity owing to their strong coupling with training resource demands. LSTM models achieve the best overall predictive accuracy but at the cost of a significantly higher number of parameters. Their complexity demands a solid grasp of architecture, sequence handling, and learning rate tuning to avoid overfitting and ensure robustness. Overall, well-chosen data-driven methods can capture the nonlinear dynamics of fluid systems and show great promise for control applications.</p>

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User oriented guide of data-driven state-space models for fluid mechanics

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Gulliver Van Essche,
  • Tim De Troyer,
  • Mark C. Runacres,
  • Jan Decuyper

摘要

The rapid expansion of machine learning has produced a wide range of data-driven methods that may be applied to unsteady fluid mechanics. The vast amount of options may overwhelm users in fluid mechanics when choosing the most suitable method for their problem. This work establishes user guidelines by investigating five widely used techniques: Dynamical Mode Decomposition with Control (DMDc), Sparse Identification of Nonlinear Dynamics (SINDy), Discrete Timestepping Multilayer Perceptron (MLP), State-Space Neural Network (SS-NN), and Long Short-Term Memory neural networks (LSTM). The methods are presented within a common state-space framework to highlight their similarities and differences. Their ability to produce accurate long-term predictions of wake variables for control implementation is evaluated via the high-dimensional, unsteady, and nonlinear fluid mechanics system of a flow past an oscillating cylinder. During the modelling process, practical recommendations are provided to help users enhance model performance. The main findings are as follows: DMDc offers a reliable, interpretable, and efficient linear baseline model. SINDy’s performance depends on careful selection of basis functions and is sensitive to coordinate space used to represent the dynamics; while powerful for low-complexity systems, it struggles with stability in complex dynamics. MLP are the simplest form of NN-based model but require multiple hidden layers leading to a strong impact of the parameter initialisation on the performance. SS-NN models require careful tuning of model complexity owing to their strong coupling with training resource demands. LSTM models achieve the best overall predictive accuracy but at the cost of a significantly higher number of parameters. Their complexity demands a solid grasp of architecture, sequence handling, and learning rate tuning to avoid overfitting and ensure robustness. Overall, well-chosen data-driven methods can capture the nonlinear dynamics of fluid systems and show great promise for control applications.