使用normal forms和科学机器学习进行颤振振荡的降阶建模
Reduced-order modelling of flutter oscillations using normal forms and scientific machine learning
摘要：
本文介绍了一种机器学习方法，采用非线性微分方程模型，在一系列参数值范围内与物理实验定性一致，并产生一个混合模型，也表现出定量一致。其基本思想是，实验的分叉实验结构可以使用诸如基于控制的延续等技术来揭示，然后用于生成简化的标准形模型。然后使用机器学习方法来学习从标准形模型到实验的物理坐标的坐标变换。该方法在气动弹性颤振的数学模型上得到了验证，在分叉图的水平上，混合模型和基本的地面实况之间显示出良好的一致性。此外，即使在远离训练数据的区域中，也精确地再现各个相位图和时间序列。因此，该方法具有显着的承诺，生产定量准确的模型，表现出正确的非线性行为的参数值的范围内。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
