Applied Mathematics, Computing and Machine Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 615

Special Issue Editor


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Guest Editor
Industrial Engineering Department, Universidad Tecnológica Metropolitana, Santiago 7800002, Chile
Interests: data analytics; smart logistic; knowledge engineering; decision making; strategic management

Special Issue Information

Dear Colleagues,

The following Special Issue of Mathematics focuses on integrating advanced mathematical methods with machine learning (ML) and deep learning (DL) techniques to address challenges in supply chain management (SCM) and industrial decision-making within the context of Industry 4.0 and 5.0. We expect contributions to demonstrate how mathematics can serve as a foundation for developing data-driven models that enhance predictive performance, operational efficiency, and strategic decision-making. Topics of interest include the use of physics-informed neural networks (PINNs), mathematical modeling of nonlinear systems, the implementation of KPIs and DSSs, and the design of trustworthy architectures for real-time industrial applications. In addition, this issue welcomes works that address dependable techniques and blockchain-based frameworks and their integration with ML/DL models to improve traceability, secure data exchange, and collaborative processes in industrial environments. Authors are encouraged to submit original research or review articles that highlight innovative approaches with clear mathematical foundations and industrial relevance.

Dr. Claudia Durán San Martín
Guest Editor

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Keywords

  • physics-informed neural networks
  • deep learning
  • machine learning
  • mathematical modeling
  • data analytics
  • multi-criteria optimization
  • blockchain integration
  • Industry 4.0 and 5.0

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Published Papers (1 paper)

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Research

25 pages, 44682 KiB  
Article
Data-Driven Solutions and Parameters Discovery of the Chiral Nonlinear Schrödinger Equation via Deep Learning
by Zekang Wu, Lijun Zhang, Xuwen Huo and Chaudry Masood Khalique
Mathematics 2025, 13(15), 2344; https://doi.org/10.3390/math13152344 - 23 Jul 2025
Viewed by 66
Abstract
The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse [...] Read more.
The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse problems of 1D and 2D CNLSEs. Specifically, a hybrid optimization strategy incorporating exponential learning rate decay is proposed to reconstruct data-driven solutions, including bright soliton for the 1D case and bright, dark soliton as well as periodic solutions for the 2D case. Moreover, we conduct a comprehensive discussion on varying parameter configurations derived from the equations and their corresponding solutions to evaluate the adaptability of the PINNs framework. The effects of residual points, network architectures, and weight settings are additionally examined. For the inverse problems, the coefficients of 1D and 2D CNLSEs are successfully identified using soliton solution data, and several factors that can impact the robustness of the proposed model, such as noise interference, time range, and observation moment are explored as well. Numerical experiments highlight the remarkable efficacy of PINNs in solution reconstruction and coefficient identification while revealing that observational noise exerts a more pronounced influence on accuracy compared to boundary perturbations. Our research offers new insights into simulating dynamics and discovering parameters of nonlinear chiral systems with deep learning. Full article
(This article belongs to the Special Issue Applied Mathematics, Computing and Machine Learning)
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