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The dynamical analysis for two-dimensional magnetic bearing system under α-stable Lévy noise excitation based on PINNs

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  • Ma, Shaojuan
  • Li, Baolan
  • Li, Hufei

Abstract

This paper mainly investigates the impact of α-stable Lévy white noise on magnetic bearing systems. By using the Physics-informed neural networks (PINNs) algorithm to solve the time-dependent Fokker–Planck-Kolmogorov (FPK) equation, the transient probability density function (PDF) is ultimately obtained. Firstly, the model of magnetic bearing system excited by α-stable Lévy white noise is established. Secondly, the fractional FPK equation for this model under the excitation of α-stable Lévy white noise is derived. Thirdly, a deep learning method based on PINNs is proposed to solve the corresponding fractional FPK equation. Finally, the effectiveness and feasibility of this method are verified through detailed examples. The results show that the PINNs solution is very consistent with the Monte Carlo (MC) results, which shows that PINNs method is suitable for solving the two-dimension space fractional FPK equation, and proves that PINNs algorithm is not only efficient in calculation, but also effective and interpretable.

Suggested Citation

  • Ma, Shaojuan & Li, Baolan & Li, Hufei, 2025. "The dynamical analysis for two-dimensional magnetic bearing system under α-stable Lévy noise excitation based on PINNs," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925011191
    DOI: 10.1016/j.chaos.2025.117106
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