Application of Computational Mathematics and Artificial Intelligence in Numerical Simulations

Dear Colleagues,

This Special Issue aims to present recent advances in computational mathematics and artificial intelligence that are transforming modern numerical simulation practices. With the rapid growth of data-driven modeling, machine learning, and Physics-Informed Neural Networks (PINNs), researchers now have powerful tools for enhancing predictive accuracy, accelerating simulations, and addressing complex physical problems that are difficult to solve using traditional methods alone.

The focus of this Special Issue includes the development of innovative numerical algorithms, optimization strategies, and hybrid AI frameworks that incorporate physical laws into learning models. In particular, PINNs have emerged as an effective approach for embedding governing equations directly into neural networks, offering new pathways for solving multiphysics problems such as fluid flow, heat transfer, structural mechanics, and coupled systems.

We welcome submissions that provide theoretical contributions, algorithmic improvements, or application-oriented studies demonstrating how AI techniques—combined with computational mathematics and simulation-based methodologies—advance scientific understanding and engineering analysis. Both original research papers and comprehensive review articles are encouraged.

Dr. Mudassar Razzaq
Prof. Dr. Marcel Gurris
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 250 words) can be sent to the Editorial Office for assessment.

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. AppliedMath is an international peer-reviewed open access monthly 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 1200 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.