Mathematical Modeling and Models in Engineering

Dear Colleagues,

Modern engineering increasingly relies on mathematical modeling to make predictions and represent reality—whether to support decision-making in system design or to understand system behavior. Mathematical models play a dual role: they both represent aspects of reality and serve as tools for extracting quantitative parameters.

This Special Issue aims to gather cutting-edge contributions to mathematical modeling and analysis of the physical systems relevant to engineering applications. We focus on models governed by partial differential equations (PDEs) that arise in fields such as solid and structural mechanics, wave propagation, thermomechanics, and fluid–structure interaction.

We are particularly interested in works that combine physical insight with mathematical rigor—employing tools from applied analysis, variational methods, and numerical simulation—to address both direct and inverse problems. Contributions may include theoretical investigations, computational methods, or application-driven studies, provided that they demonstrate methodological innovation and clear relevance to engineering challenges. We also welcome studies that explore how techniques from machine learning and artificial intelligence can be integrated with physics-based models to enhance prediction, parameter identification, or real-time control.

Topics of interest include (but are not limited to) the following:

• Forward and inverse problems in continuum mechanics and wave phenomena;
• Mathematical modeling of elastic, acoustic, and thermoelastic systems;
• Parameter identification, source reconstruction, and optimal design;
• Variational formulations, asymptotic analysis, and model reduction;
• Coupled multiphysics problems and interface modeling;
• Numerical methods with mathematical guarantees (e.g., stability, convergence);
• Simulation of fracture, damage, and nonlinear material behavior;
• Integration of AI/machine learning techniques with mathematical models for engineering applications.

This Special Issue promotes research that advances mathematical understanding while providing impactful solutions to real-world engineering problems, including the intelligent modeling and control of complex systems.

Prof. Alexandre Kawano
Prof. Antonino Morassi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• inverse problems
• mathematical modeling
• numerical methods
• ai/machine learning techniques
• interface modeling
• parameter identification
• source reconstruction
• optimal design
• model reduction
• variational formulations
• asymptotic analysis