https://doi.org/10.1140/epjs/s11734-024-01344-7
Regular Article
Tracking global topologies by deep learning-based progressive training with few data
1
College of Sciences, Xi’an University of Science and Technology, 710054, Xi’an, Shaanxi, People’s Republic of China
2
State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, People’s Republic of China
Received:
23
June
2024
Accepted:
16
September
2024
Published online:
23
September
2024
The global dynamical structures of a nonlinear system and its topological behaviors indicate the intrinsic mechanisms governing their responses’ occurrences and evolutions. To mitigate the prohibitive costs associated with resampling in model-based and test-based global topology analysis, this paper proposes a robust and efficient neural network approximation for short-time responses of nonlinear system under the framework of deep learning. By integrating with the generalized cell mapping (GCM) method, the underlying global structures are revealed from one-step transition probability matrix, which can be generated by predicted short-time responses. As the system’s parameter gradually shifts, the slight deviation in short-time response can be detected at a specified cell level. The dynamics of the derived system can be approximated by the fine-tuning hyperparameters on the base of pre-trained surrogate model. This allows for progressively tracking the changes in system’s topological behaviors, merely using few samples. The progressive training and optimization of hyperparameters have proven to be highly efficient and low-cost for tracking global topologies. Three representative examples with parameter-induced local and global bifurcations are taken to demonstrate the performance of the proposed method. Additionally, the effects of sample sizes on prediction accuracy during progressive training are discussed.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
