Advances in Mathematical Approaches to Trustworthy and Secure AI Systems

Dear Colleagues,

Rapid developments in artificial intelligence (AI) have led to transformative innovations across sectors such as healthcare, finance, transportation, and public services. However, the widespread deployment of AI systems raises critical concerns about their trustworthiness, encompassing their reliability, robustness, fairness, transparency, accountability, privacy, and security.

Ensuring AI trustworthiness demands not only ethical and regulatory frameworks, but also solid mathematical foundations and computational models that can rigorously characterize, analyze, and enhance the behavior of AI systems. Mathematical tools such as optimization theory, probability and statistics, game theory, differential privacy, dynamical systems, and computational geometry play a central role in addressing issues of AI robustness, fairness, interpretability, and security.

This Special Issue invites submissions of high-quality research papers, surveys, and position articles that advance the mathematical, theoretical, and algorithmic understanding of trustworthy AI. We seek contributions that propose new models, frameworks, computational techniques, and interdisciplinary approaches that leverage mathematical methods to address emerging challenges in AI trustworthiness.

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

• Mathematical models for AI reliability and robustness:
  • Adversarial risk analysis and formal robustness guarantees;
  • Probabilistic and statistical validation of AI models;
  • Game theoretic frameworks for adversarial learning;
  • Mathematical frameworks for safe and resilient AI.
• Fairness, transparency, and explainability:
  • Fairness-aware optimization and bias quantification;
  • Explainable AI through interpretable mathematical models;
  • Algorithmic auditing and mathematical accountability mechanisms;
  • Human-in-the-loop decision processes modeled mathematically.
• Privacy-preserving and secure AI:
  • Differential privacy, homomorphic encryption, and secure multiparty computation;
  • Federated learning algorithms and privacy-aware distributed optimization;
  • Formal methods for data provenance and integrity in AI pipelines.
• Trust modeling and human–AI interactions:
  • Mathematical models for trust quantification in AI systems;
  • User trust calibration models and probabilistic trust metrics;
  • Computational frameworks for transparent AI interfaces.
• Emerging mathematical challenges in AI security and ethics:
  • Quantum-resilient AI algorithms and security implications;
  • Trust and security in AI-powered digital twins and multi-agent systems;
  • Optimization-based frameworks for sustainable and responsible AI.

We look forward to receiving your contributions that reflect the mathematical rigor and theoretical depth required for developing trustworthy AI systems.

Dr. Yang Liu
Guest Editor

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.

• trustworthy AI
• mathematical foundations
• AI fairness and explainability
• privacy-preserving AI
• secure and robust AI
• federated learning