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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.15181 |
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| _version_ | 1866917414167379968 |
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| author | Ma, Teng Rosafalco, Luca Cui, Wei Zhao, Lin Frangi, Attilio |
| author_facet | Ma, Teng Rosafalco, Luca Cui, Wei Zhao, Lin Frangi, Attilio |
| contents | Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning governing equations. We introduce MEv-SINDy (Multi-frequency Evolutionary Sparse Identification of Nonlinear Dynamics) to infer the governing equations of non-autonomous and multi-frequency systems. The methodology leverages the Generalized Harmonic Balance (GHB) method to decompose complex forced responses into a set of slow-varying evolution equations. We validated the capabilities of MEv-SINDy on two critical Micro-Electro-Mechanical Systems (MEMS). These applications include a nonlinear beam resonator and a MEMS micromirror. Our results show that the model trained on a single point accurately predicts softening/hardening effects and jump phenomena across a wide range of excitation levels. This approach significantly reduces the data acquisition burden for the characterization and design of nonlinear microsystems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15181 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators Ma, Teng Rosafalco, Luca Cui, Wei Zhao, Lin Frangi, Attilio Machine Learning Dynamical Systems Extrapolative prediction of complex nonlinear dynamics remains a central challenge in engineering. This study proposes a one-shot learning method to identify global frequency-response curves from a single excitation time history by learning governing equations. We introduce MEv-SINDy (Multi-frequency Evolutionary Sparse Identification of Nonlinear Dynamics) to infer the governing equations of non-autonomous and multi-frequency systems. The methodology leverages the Generalized Harmonic Balance (GHB) method to decompose complex forced responses into a set of slow-varying evolution equations. We validated the capabilities of MEv-SINDy on two critical Micro-Electro-Mechanical Systems (MEMS). These applications include a nonlinear beam resonator and a MEMS micromirror. Our results show that the model trained on a single point accurately predicts softening/hardening effects and jump phenomena across a wide range of excitation levels. This approach significantly reduces the data acquisition burden for the characterization and design of nonlinear microsystems. |
| title | One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators |
| topic | Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2604.15181 |