Linghongzhi Lu
(, ), Yang Li
(, ), Xianbin Liu
(, )
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引用次数: 0
Abstract
The burgeoning data-driven techniques endow large potential to predict fairly practical or complex dynamical systems in various fields through massive data. Lévy noise, a more universal and intricate fluctuation model comparing with Gaussian white noise, is widely employed in many non-Gaussian cases to mimic bursting or hopping. In this manuscript, we present a systematic data-driven method to identify the most probable exit trajectory of a system that is perturbed both by Gaussian white noise and non-Gaussian Lévy noise. The main theoretical and numerical conceptions involve a set of extended Kramers-Moyal formulas and the Kolmogorov forward equation in classic dynamical systems theory as well as a supervise learning theory to solve the fitting problems by using the Cross Validation. We then give two examples to show the feasibility in detail, and do a brief bifurcation analysis for the most probable exit trajectory. The above approach will serve as a numerical correspondence to as well as verification for the relative theoretical research, and provide a referential resolution to the numerical identification of more transition indicators of this complex system, which is more general than the Gaussian diffusion process.
期刊介绍:
Acta Mechanica Sinica, sponsored by the Chinese Society of Theoretical and Applied Mechanics, promotes scientific exchanges and collaboration among Chinese scientists in China and abroad. It features high quality, original papers in all aspects of mechanics and mechanical sciences.
Not only does the journal explore the classical subdivisions of theoretical and applied mechanics such as solid and fluid mechanics, it also explores recently emerging areas such as biomechanics and nanomechanics. In addition, the journal investigates analytical, computational, and experimental progresses in all areas of mechanics. Lastly, it encourages research in interdisciplinary subjects, serving as a bridge between mechanics and other branches of engineering and the sciences.
In addition to research papers, Acta Mechanica Sinica publishes reviews, notes, experimental techniques, scientific events, and other special topics of interest.
Related subjects » Classical Continuum Physics - Computational Intelligence and Complexity - Mechanics