Reduced-order modelling of flutter oscillations using normal forms and scientific machine learning

TL;DR

This paper presents a hybrid modeling approach combining normal forms and machine learning to accurately replicate nonlinear flutter oscillations across parameter ranges, improving upon purely theoretical or empirical models.

Contribution

It introduces a novel method that uses control-based continuation and machine learning to create hybrid models with both qualitative and quantitative agreement with experiments.

Findings

Accurately reproduces bifurcation diagrams.

Replicates phase portraits and time series.

Demonstrates effectiveness on aero-elastic flutter model.

Abstract

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.