AI-Driven Computational Methods: Theories, Algorithms and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".
Deadline for manuscript submissions: 29 May 2026 | Viewed by 5
Special Issue Editors
Interests: computational mechanics; numerical analysis; boundary element method; meshless method; acoustic propagation; heat and mass transfer
Special Issues, Collections and Topics in MDPI journals
Interests: solid mechanics; computational mechanics; meshless method; wave propagation
Special Issues, Collections and Topics in MDPI journals
Interests: computational mechanics; mesh-free methods; advanced finite element methods; vibration and wave propagation in composite structures; acoustic problems; numerical analysis; machine learning
Special Issue Information
Dear Colleagues,
In recent decades, numerical methods have served as the foundation for computational mathematics, providing reliable tools for simulating and solving a wide range of scientific and engineering problems. However, the increasing complexity of real-world systems, which are characterized by large-scale, nonlinear, and multi-physics models, has pushed traditional methods to their limits in terms of accuracy, adaptability, and computational efficiency. Meanwhile, the rapid development of artificial intelligence (AI), supported by the explosive growth of data resources, powerful computing hardware, and breakthroughs in machine learning and neural networks, has opened new possibilities for addressing these challenges. AI not only accelerates simulations, but also enables the creation of hybrid approaches that integrate data-driven intelligence with established numerical frameworks. These developments highlight the necessity of systematically exploring AI-driven computational methods in order to both advance theoretical foundations and expand practical capabilities in scientific computation.
This Special Issue of Mathematics (MPDI), “AI-Driven Computational Methods: Theories, Algorithms and Applications”, aims to collect cutting-edge research at the intersection of AI and numerical computation, showcasing innovations in theory, algorithm development, simulation strategies, and applications across scientific disciplines. We invite original research articles and comprehensive reviews that present novel methodologies or significant applications of AI in numerical and computational methods. Topics of interest include, but are not limited to, neural-network-enhanced numerical methods; machine learning for PDEs and ODEs; data-driven finite element and finite difference methods; surrogate modeling and reduced-order models; meshless and particle-based methods with AI support; AI-assisted optimization and inverse problems; convergence and error analysis of AI-integrated schemes; adaptive algorithms guided by AI or reinforcement learning; high-performance computing for AI-based simulations; hybrid frameworks combining traditional solvers with AI models; and applications in computational mechanics, physics-based simulatons, biology, and engineering.
Prof. Dr. Fajie Wang
Prof. Dr. Ji Lin
Prof. Dr. Yingbin Chai
Guest Editors
Manuscript Submission Information
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Keywords
- AI-driven computational methods
- machine learning for numerical analysis
- neural network algorithms
- data-driven PDE solvers
- physics-informed neural networks
- generative adversarial networks
- hybrid methods combining traditional numerical approaches and AI
- surrogate models
- optimization
- adaptive algorithms
- error estimation
- high-performance computing
- computational mechanics
- scientific computing
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