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State estimation for stochastic delayed neural networks with diffusion terms: A two-step estimation method.

Yu Gao¹, Zhi-Yun Zhang², Xiao-Zhen Liu³

¹Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, China.

Neural Networks : the Official Journal of the International Neural Network Society

|November 26, 2025

Summary

This summary is machine-generated.

This study introduces a new two-step interval estimation method for stochastic delayed reaction-diffusion neural networks. The approach provides interval estimations for the expected solution value, enhancing traditional point estimation techniques.

Keywords:

Neural networks Peak-to-peak analysis Reaction-diffusion system State estimation Two-step estimation

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Area of Science:

Neural Networks
Stochastic Systems
Control Theory

Background:

Stochastic delayed reaction-diffusion neural networks are complex systems requiring accurate state estimation.
Traditional point estimation methods may not fully capture the uncertainty in these systems.
Interval estimation offers a more comprehensive understanding of system behavior by providing bounds.

Purpose of the Study:

To propose a novel two-step interval estimation scheme for stochastic delayed reaction-diffusion neural networks.
To move beyond traditional point estimation by providing interval estimations of the solution's expected value.
To develop adaptive thresholds for system state estimation based on observations and error bounds.

Main Methods:

A robust observer is utilized for the initial pointwise expected value computation.
An auxiliary functional is introduced to derive the bounds of the observation error.
Adaptive thresholds are synthesized using observations and derived error bounds; observer gain design influences both point estimation accuracy and interval width.
Peak-to-peak analysis is employed to manage computational complexity in high-dimensional systems.

Main Results:

The proposed two-step method successfully yields interval estimations for the expected value of the solution.
The observer gain design effectively balances point estimation accuracy and the width of the error interval.
Numerical simulations confirm the efficacy of the developed interval estimation scheme.

Conclusions:

The novel two-step interval estimation method provides a robust approach for analyzing stochastic delayed reaction-diffusion neural networks.
The technique enhances system state estimation by offering interval bounds, crucial for understanding system uncertainty.
The method demonstrates practical applicability through successful numerical validation, offering a valuable tool for researchers in the field.