A noise-tolerant zeroing neural network with fixed-time convergence for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors

Ruijuan Zhao; Mengyao Li; Tingjia Liu; Shu-Xin Miao; Ruijuan Zhao; Mengyao Li; Tingjia Liu; Shu-Xin Miao

doi:10.3934/math.2025628

AIMS Mathematics

2025, Volume 10, Issue 6: 13974-13995. doi: 10.3934/math.2025628

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Research article

A noise-tolerant zeroing neural network with fixed-time convergence for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors

1.
School of Information Engineering and Artiffcial Intelligence, Lanzhou University of Finance and Economics, Lanzhou 730101, China
2.
School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 01 April 2025 Revised: 28 May 2025 Accepted: 06 June 2025 Published: 18 June 2025
MSC : 15A69, 65F15, 68W25

Multi-linear systems play a crucial role in various practical applications such as high-dimensional partial differential equations (PDEs), signal processing, and high-order statistics. In this paper, we propose a noise-tolerant zeroing neural network (NTZNN) model with fixed-time convergence activated by a new nonlinear activation function for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors. The detailed theoretical analysis demonstrates that the NTZNN model is stable in the sense of Lyapunov stability theory and achieves fixed-time convergence with or without the presence of noises. Furthermore, compared with existing neural network models, the proposed NTZNN model significantly improves the convergence rate while maintaining noise tolerance. Numerical experiments further show the effectiveness and superiority of the proposed NTZNN model.
- zeroing neural network,
- multi-linear systems,
- fixed-time convergence,
- noise-tolerant,
- nonsingular $ \mathcal{M} $-tensors
Citation: Ruijuan Zhao, Mengyao Li, Tingjia Liu, Shu-Xin Miao. A noise-tolerant zeroing neural network with fixed-time convergence for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors[J]. AIMS Mathematics, 2025, 10(6): 13974-13995. doi: 10.3934/math.2025628

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Abstract

Multi-linear systems play a crucial role in various practical applications such as high-dimensional partial differential equations (PDEs), signal processing, and high-order statistics. In this paper, we propose a noise-tolerant zeroing neural network (NTZNN) model with fixed-time convergence activated by a new nonlinear activation function for solving multi-linear systems with nonsingular $ \mathcal{M} $-tensors. The detailed theoretical analysis demonstrates that the NTZNN model is stable in the sense of Lyapunov stability theory and achieves fixed-time convergence with or without the presence of noises. Furthermore, compared with existing neural network models, the proposed NTZNN model significantly improves the convergence rate while maintaining noise tolerance. Numerical experiments further show the effectiveness and superiority of the proposed NTZNN model.

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