Applied Mathematical Modeling and Machine Learning for Geomechanics and Superconducting Materials

A special issue of AppliedMath (ISSN 2673-9909). This special issue belongs to the section "Computational and Numerical Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 939

Special Issue Editors


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Guest Editor
School of Petrochemical Engineering, Lanzhou University of Technology, Lanzhou, China
Interests: rock mechanics; soil-rock mixtures; freeze thaw cycle; particle flow code

E-Mail Website
Guest Editor
School of Petrochemical Engineering, Lanzhou University of Technology, Lanzhou, China
Interests: coupled field theory and numerical computation​; solid mechanics of superconducting structures; blasting control technology; artificial intelligence algorithms

Special Issue Information

Dear Colleagues,

We invite you to submit your research results for publication in this Special Issue of AppliedMath, focusing on the latest advances in the intersection of machine learning, geomechanics, and superconducting mechanics. This Special Issue will showcase the latest advancements in the field and provide a platform for researchers to share their promising findings.

The combination of machine learning and geomechanics has been the most popular research topic in this field in recent years. Machine learning provides varied techniques and ideas for data preprocessing, feature extraction, model selection of rocks, concrete, superconducting materials, etc. By deeply integrating traditional geomechanics, superconducting mechanics, and machine learning, more accurate mathematical models can be proposed to meet the challenges of scientific research and engineering applications in the era of big data.

In this Special Issue, we invite and welcome original papers on machine learning, geomechanics, superconductivity, etc.

Dr. Guanglin Tian
Dr. Wenhai Zhou
Dr. Taoying Liu
Guest Editors

Manuscript Submission Information

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Keywords

  • discrete element method
  • machine learning
  • deep learning
  • mathematical model
  • rock mechanics
  • superconducting mmechanics
  • soil–rock mixture mechanics

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Published Papers (1 paper)

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Research

24 pages, 9493 KB  
Article
A Benchmarking Study for Algorithm Selection in Scientific Machine Learning (SciML): PINN vs. gPINN for Solving Partial Differential Equations
by Muhammad Azam, Imran Shabir Chuhan, Muhammad Shafiq Ahmed and Kaleem Arshid
AppliedMath 2026, 6(2), 26; https://doi.org/10.3390/appliedmath6020026 - 9 Feb 2026
Cited by 1 | Viewed by 608
Abstract
Recent advances in physics-informed neural networks (PINN) have highlighted the need for systematic criteria for selecting appropriate algorithms to solve differential equations. This paper presents a numerical comparison between standard PINNs and gradient-enhanced PINNs (gPINNs) used to solve a high-order partial differential equations [...] Read more.
Recent advances in physics-informed neural networks (PINN) have highlighted the need for systematic criteria for selecting appropriate algorithms to solve differential equations. This paper presents a numerical comparison between standard PINNs and gradient-enhanced PINNs (gPINNs) used to solve a high-order partial differential equations (PDE). To verify the accuracy and convergence behavior of all the methods, we solve a fourth-order PDE whose analytical solution is known. gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. We synthesize our findings into a practical selection guide; gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. This framework provides a clear, evidence-based policy for algorithm choice in SciML. Beyond numerical comparison, we provide an analytical interpretation linking solver performance to the spectral and stiffness properties of each PDE class, offering a principled basis for algorithm selection. Full article
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