Manuscript Topics

1. Introduction

Artificial intelligence (AI) has profound impact on sciences such as imaging sciences, protein and antibody design, and partial differential equations (PDEs). In imaging sciences, AI-driven algorithms have revolutionized image processing, offering superior image reconstruction, segmentation, and enhancement capabilities, which has paved the way for more accurate diagnostics and nuanced visual data interpretation.

For protein and antibody design, AI has ushered in a new era by predicting protein folding and inverse folding and molecular interactions with high precision, dramatically accelerating the drug discovery process and enabling the design of therapeutic agents with unprecedented precision. When applied to PDEs, AI aids in the approximation of solutions for complex and high-dimensional equations that were once deemed computationally intractable. The explosive growth in artificial intelligence (AI), imaging sciences, protein and antibody design, and biology demands a renewed focus on the underlying mathematics that powers these fields. This special issue proposes an in-depth exploration of numerical and computational mathematics as it relates to contemporary applications in these burgeoning domains. It would facilitate cross-disciplinary collaborations, enhance our understanding of computational mathematics in contemporary applications, and inspire the next generation of mathematical frameworks and tools tailored for emerging technological challenges.

2. Potential Topics

To spotlight the latest advancements, challenges, and intersections of numerical and computational mathematics with topics but not limited to  
a) Mathematics of Artificial Intelligence  
b) Computational Mathematics of Imaging Sciences  
c) Computational Methods of AI for Protein and Antibody Design and Drug Discovery  
d) Numerical Analysis of Deep Learning for Partial Differential Equations (PDE)  
e) PDE for Biology

a). Mathematics of Artificial Intelligence:
• Novel algorithms bridging machine learning and numerical analysis
• Optimization techniques in deep learning
• Mathematical underpinnings of AI architectures
• Approximation theory
• Harmonic analysis
• Algebraic statistics
• Combinatorics
• Differential geometry
• Information geometry
• Statistical computing

b). Computational Mathematics of Imaging Sciences:
• Inverse problems and imaging
• Computational methods for image reconstruction
• Mathematical modeling in imaging technologies

c). Computational Methods of AI for Protein and Antibody Design and Drug Discovery:
• AI-powered algorithms for protein folding and inverse folding
• Computational methods for predicting protein structures
• Mathematical modeling in biomolecular design
• Algorithmic analysis for drug discovery

d). Numerical Analysis of AI for PDE:
• AI-enhanced solvers for complex PDEs
• Neural network representations of PDEs
• Hybrid models combining traditional PDE solvers with AI techniques
• Convergence of NN-based solu$on to PDEs

e). PDE for Biology:
• PDE models for biological processes
• Numerical methods tailored for biological applications
• Analysis of PDE solutions in biological contexts

Instructions for authors
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Please submit your manuscript to online submission system
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