Compressive-sensing model reconstruction of nonlinear systems with multiple attractors

Sun, Xiuting; Qian, Jiawei; Xu, Jian

doi:10.1016/j.ijmecsci.2023.108905

International Journal of Mechanical Sciences

2024

DOI: 10.1016/j.ijmecsci.2023.108905

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Compressive-sensing model reconstruction of nonlinear systems with multiple attractors

Xiuting Sun,

Jiawei Qian,

Jian Xu

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Cited by 5 publications

References 73 publications

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Automating the discovery of partial differential equations in dynamical systems

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Identifying partial differential equations (PDEs) from data is crucial for understanding the governing mechanisms of natural phenomena, yet it remains a challenging task. We present an extension to the ARGOS framework, ARGOS-RAL, which leverages sparse regression with the recurrent adaptive lasso to identify PDEs from limited prior knowledge automatically. Our method automates calculating partial derivatives, constructing a candidate library, and estimating a sparse model. We rigorously evaluate the performance of ARGOS-RAL in identifying canonical PDEs under various noise levels and sample sizes, demonstrating its robustness in handling noisy and non-uniformly distributed data. We also test the algorithm's performance on datasets consisting solely of random noise to simulate scenarios with severely compromised data quality. Our results show that ARGOS-RAL effectively and reliably identifies the underlying PDEs from data, outperforming the sequential threshold ridge regression method in most cases. We highlight the potential of combining statistical methods, machine learning, and dynamical systems theory to automatically discover governing equations from collected data, streamlining the scientific modeling process.

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Compressive-sensing model reconstruction of nonlinear systems with multiple attractors

Cited by 5 publications

References 73 publications

Discovering differential governing equations of hysteresis dynamic systems by data-driven sparse regression method

Discovering differential governing equations of hysteresis dynamic systems by data-driven sparse regression method

Magnetic coupling and amplitude truncation based bistable energy harvester

Automating the discovery of partial differential equations in dynamical systems

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