# One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators

arXiv: https://arxiv.org/abs/2604.15181 · HTML: https://mlsanity.com/paper/2604.15181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Data-driven Discovery of Cyber-Physical Systems](https://mlsanity.com/paper/1810.00697/) (2018)
- [Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference](https://mlsanity.com/paper/2401.16943/) (2024)
- [Discovering physical laws with parallel symbolic enumeration](https://mlsanity.com/paper/2407.04405/) (2024)
- [Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples](https://mlsanity.com/paper/2005.11699/) (2020)

## Abstract (arXiv)

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.