Advances in Computational Oncology: Mathematical Modeling, Numerical Methods, and Intelligent Systems

Dear Colleagues,

Cancer remains one of the most complex and devastating diseases worldwide, and the development of accurate, predictive computational models is pivotal to advancing our understanding of tumor initiation, progression, invasion, and response to therapy. The inherent multi-scale and multi-physics nature of tumor dynamics—spanning molecular signaling, cellular mechanics, tissue-level remodeling, and macroscopic growth—demands a synergistic integration of advanced mathematical frameworks, state-of-the-art numerical methods, and modern data-driven approaches.

This Special Issue aims to collect high-quality, original contributions that present innovative numerical, mathematical, and deep learning methodologies for modeling and simulating tumor-related phenomena across diverse biological environments. The scope includes, but is not limited to, the following themes:

• Partial differential equation (PDE) models for tumor growth, invasion, and metastasis in heterogeneous tissue environments, including avascular and vascular settings.
• Reaction-diffusion and chemotaxis systems describing tumor angiogenesis, nutrient transport, extracellular matrix degradation, and cell–cell interactions.
• Novel numerical schemes for stiff, multi-scale biological systems, including positivity-preserving schemes, operator-splitting techniques, and adaptive mesh refinement strategies.
• Physics-informed neural networks and neural operators for the forward and inverse solution of PDE-based tumor models.
• Deep learning architectures, convolutional neural networks, graph neural networks, and transformers—applied to tumor classification, progression prediction, and treatment optimization.
• High-performance and GPU-accelerated computing strategies for large-scale tumor simulations.
• Fractional-order and non-local models capturing anomalous diffusion and memory effects in tumor microenvironments.
• Uncertainty quantification, sensitivity analysis, and Bayesian inference for parameter estimation in tumor models.
• Hybrid continuum–discrete and agent-based models coupled with machine learning surrogates for multi-scale tumor dynamics.
• Digital twins and patient-specific simulation frameworks integrating clinical imaging data with computational models for personalized oncology.

We welcome both methodological advances and application-driven studies that demonstrate the potential of innovative computational techniques in realistic tumor scenarios. Contributions showcasing rigorous mathematical analysis, efficient numerical implementations, validation against experimental or clinical data, and interdisciplinary collaborations between mathematicians, computer scientists, engineers, and biomedical researchers are particularly encouraged.

We look forward to receiving your contributions and to assembling a collection of works that reflects the state of the art and future directions in computational tumor modeling.

Kind regards,

Dr. Pasquale De Luca

Dr. Annabella Di Mauro

Dr. Annabella Di Mauro
Dr. Pasquale De Luca
Guest Editors

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• tumor modeling
• numerical methods for PDEs
• deep learning in oncology
• physics-informed neural networks
• chemotaxis–reaction–diffusion systems
• tumor angiogenesis
• high-performance computing
• positivity-preserving schemes
• neural operators
• fractional differential equations
• multi-scale biological models
• GPU-accelerated simulation
• computational oncology
• uncertainty quantification