论文标题
使用正常形式和科学机器学习对颤动振荡的降低建模
Reduced-order modelling of flutter oscillations using normal forms and scientific machine learning
论文作者
论文摘要
本文介绍了一种机器学习方法，以采用非线性差分方程模型，该模型在一系列参数值上与物理实验表现出定性一致，并产生一个混合模型，该模型也表现出定量一致。基础思想是，可以使用基于对照的延续等技术来揭示实验的分叉实验结构，然后用于生成简化的正常形式样模型。然后，使用机器学习方法来学习从正常形式模型到实验的物理坐标的坐标转换。这种方法是在空气弹性颤音的数学模型上证明的，其中在混合模型和基础地面真理之间显示了分叉图的良好一致性。此外，即使在远离训练数据的区域，个人相肖像和时间序列也可以准确地重现。因此，该方法具有产生定量准确模型的重要希望，这些模型在一系列参数值上表现出正确的非线性行为。
This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits quantitative agreement. The underpinning idea is that the bifurcation experiment structure of an experiment can be revealed using techniques such as control-based continuation and then used to generate a simplified normal-form-like model. A machine learning approach is then used to learn a coordinate transform from the normal-form-like model to the physical coordinates of the experiment. This approach is demonstrated on a mathematical model of aero-elastic flutter, where good agreement at the level of the bifurcation diagrams is shown between the hybrid model and the underlying ground truth. Moreover, individual phase portraits and time series are also reproduced accurately, even in regions away from training data. As such, the approach holds significant promise for producing quantitatively accurate models that exhibit the correct nonlinear behaviour over a range of parameter values.
