Machine Learning: Mathematical Foundations and Applications

Dear Colleagues,

Overview

Machine Learning (ML) has emerged as a transformative force across research and industry, driven by advances in algorithms, computational power, and data availability. However, challenges such as data explosion, scalability, computational costs and manpower requirements demand the development of rigorous mathematical frameworks able to optimize efficiency and generalization. Mathematical frameworks provide the foundational theory and framework for ML algorithms. Meanwhile, mathematical modelling techniques offer efficient solutions and mechanisms that can significantly reduce the costs of large-scale training and learning.

This Special Issue invites to compile experts and scholars from related fields to present their recent research on machine learning and its mathematical foundation and applications. This Special Issue will address the development of state-of-the-art technology in the field of machine learning and mathematical optimization, as well as the future trends in this field. This Special Issue will also address several topics related to machine learning algorithms, mathematical optimization,  loss function optimization, efficient computation in large-scale ML, data mining and visualization, deep learning methods, intelligent knowledge mining, physics-informed neural networks (PINNSs), Markov random fields in probabilistic graphical models, graph neural networks (GNNs) and their applications, pattern recognition, hyperparameter tuning, regularization techniques, dimensionality reduction, and large Language Models (LLMs).

Scope and Topics

The scope of this Special Issue includes, but is not limited to, the following topics:

1. Foundations of ML and Optimization
   • Mathematical theory of ML algorithms (e.g., convergence, complexity)
   • Loss function design and optimization
   • Regularization techniques and dimensionality reduction
   • Hyperparameter tuning and model selection
2. Scalable and Efficient ML
   • Distributed/parallel computing for large-scale ML
   • Efficient training techniques (e.g., gradient compression, quantization)
   • Physics-informed neural networks (PINNs) for scientific ML
3. Advanced Learning Paradigms
   • Deep learning architectures and optimization
   • Graph neural networks (GNNs) and probabilistic graphical models (e.g., Markov random fields)
   • Large Language Models (LLMs) and knowledge mining
4. Applications and Tools
   • Data mining and visualization
   • Pattern recognition and intelligent systems
   • Real-world applications of ML in science, engineering, and industry

• Submission deadline: [31 January 2026]
• Notification of acceptance: [Manuscripts are peer-reviewed and a first decision is provided to authors approximately 18.3 days after submission; acceptance to publication is undertaken in 1.9 days (median values for papers published in this journal in the second half of 2024).]

Submission Guidelines

Authors should follow the journal’s template and submit manuscripts via [https://www.mdpi.com/journal/mathematics/instructions]. All papers will undergo peer review.

Dr. Haolan Zhang
Prof. Dr. Xingsen Li
Prof. Dr. Yunfa Fu
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.

• machine learning
• efficient computation in large-scale ML
• mathematical optimization
• PINNS
• LLM
• GNNs
• Markov random fields in probabilistic graphical models
• hyperparameter tuning