Data-driven modeling of bifurcation systems by learning the bifurcation parameter generalization
Document Type
Article
Publication Date
9-28-2024
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
Nonlinear dynamical systems in such applications as design and control often depend on a set of parameters, resulting in parameterized dynamical systems. Establishing mathematical models of such parameterized systems is essential for numerical simulations, where first-principle models are often not affordable although they are desired whenever possible. Data-driven modeling is an important alternative with a trade-off among modeling difficulty, model complexity, and computational efficiency. However, data-driven modeling of such parameterized systems is challenging because not only nonlinear dynamics but also their parametric dependence need to be identified from data; especially for bifurcation systems where small changes in the parameters may cause drastic, qualitative changes of dynamical behaviors. Thus, data-driven modeling of bifurcation systems can be intractable. This work presents a novel method for data-driven modeling of bifurcation systems by transforming the intractable modeling problem into two tractable steps: first, learning an intermediate meta-model that is general for a wide range of bifurcation parameter values; subsequently, using this meta-model to perform efficient adaptation to target/new bifurcation values. Particularly, we leverage the meta-learning to guide the intermediate model to learn to generalize over the bifurcation parameter values, yielding a meta-model which allows a fast and data-efficient adaptation (generalization) to any new bifurcation parameter values. We conduct numerical experiments to validate the presented method on three classic bifurcation systems. It is observed that the adaptation (generalization) to new parameter values enabled by the obtained meta-model is faster than the direct modeling for the new parameter values from scratch. Furthermore, the meta-model-based adaptation yields more accurate models that allow long-term future-state prediction. Finally, we discuss the limitations of this work and potential future studies needed.
Publication Title
Nonlinear Dynamics
Recommended Citation
Li, S.,
&
Yang, Y.
(2024).
Data-driven modeling of bifurcation systems by learning the bifurcation parameter generalization.
Nonlinear Dynamics.
http://doi.org/10.1007/s11071-024-10304-8
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1183