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Encoding Cumulation to Learn Perturbative Nonlinear Oscillatory Dynamics
Teng Ma1,2, Ting-Ting Gao3, Wei Cui1
1State Key Lab of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, P. R. China.
Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|March 6, 2026
Summary
A new method, Evolutionary Learning Oscillator with Weak Nonlinearity (EvLOWN), accurately identifies governing equations for weakly nonlinear systems from limited data. This approach works for complex physical and engineering applications, revealing subtle dynamics in diverse systems.
Area of Science:
- Physics
- System Identification
- Nonlinear Dynamics
Background:
- Oscillatory dynamics are fundamental across physical systems.
- Weak nonlinearities critically influence system stability and long-term behavior.
- Characterizing these nonlinearities from data is challenging due to their subtle nature.
Purpose of the Study:
- Introduce a data-driven method, EvLOWN, for inferring equations of weakly nonlinear oscillators.
- Demonstrate EvLOWN's accuracy and robustness in system identification.
- Apply EvLOWN to diverse physical and engineering problems.
Main Methods:
- Developed Evolutionary Learning Oscillator with Weak Nonlinearity (EvLOWN).
- Utilized sparse and noisy time-series observations.
- Applied to benchmark systems, theoretical models (Fermi-Pasta-Ulam, Klein-Gordon chains), and experimental data.
Main Results:
- EvLOWN accurately reconstructs governing equations for weakly nonlinear systems.
- Successfully uncovered subtle potentials in fundamental physical models.
- Reconstructed orbital dynamics of space stations and captured complex vibrations in a suspension bridge.
Conclusions:
- EvLOWN is a powerful tool for data-driven discovery in complex systems.
- Effective for systems where weak nonlinearities are crucial but subtle.
- Broad applicability in physics and engineering system identification.
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