Piecewise Physics-Constrained Neural Networks for solving second-order impulsive differential equations

Due to the reliance of traditional numerical methods on grids, their performance significantly degrades when dealing with non-linear complex problems such as impulsive problems. In contrast, as mesh-free methods, physics-informed neural networks(PINNs) have more advantages in solving impulsive probl...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) Vol. 649; p. 130764
Main Authors: Chen, Junxi, Mei, Liangcai, Yang, Chuan, Liu, Boyang, Han, Jiarong, Yao, Wulong
Format: Journal Article
Language:English
Published: Elsevier B.V 07.10.2025
Subjects:
Hard enforcement
Impulsive differential equations
Numerical algorithm
Physics-Informed Neural Networks
Physics-Informed Neural Networks
Hard enforcement
Impulsive differential equations
Numerical algorithm
ISSN:0925-2312
Online Access:Get full text
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Summary:Due to the reliance of traditional numerical methods on grids, their performance significantly degrades when dealing with non-linear complex problems such as impulsive problems. In contrast, as mesh-free methods, physics-informed neural networks(PINNs) have more advantages in solving impulsive problems. This paper proposes a model named Piecewise-PCNNs. This model adopts multiple sub-networks architecture and hard enforcement method. It realizes the transformation from multi-objective optimization to single-objective optimization through prior information and improves the model performance by decoupling the solution space. To evaluate the performance of this model, this paper selects various types of second-order impulsive differential equations and conducts numerical experiments with other numerical methods. Experiments prove that under general circumstances, the Piecewise-PCNNs model has higher computational accuracy and efficiency, and this advantage can be extended to complex non-linear impulsive problems.
ISSN:0925-2312
DOI:10.1016/j.neucom.2025.130764