Research Focus

Research Areas

Four interconnected research pillars bridging mathematical foundations with real-world AI applications.

Research Framework

Mathematical Foundations

Optimization Theory, Approximation, Dynamical Systems, Geometry of Neural Networks

Models & Algorithms

Provable DL Architectures, High-dim Optimization, Explainable AI Tools

Collaboration & Impact

International Publications (Q1-Q2), Open-source Tools, Junior Researcher Development, Real-world Deployments

Four Research Pillars

Pillar 1

High-Performance Optimization Algorithms

Developing large-scale optimization algorithms for training complex models on medical and engineering data.

Nonconvex & large-scale optimization for deep learning
Stochastic optimization with convergence guarantees
SVM with novel loss functions (Generalized Pinball, Rescaled)
Neurodynamic neural network methods
Pillar 2

Provable Deep Learning Architectures

Designing new deep learning architectures with provable mathematical properties — convergence, stability, and generalization bounds.

Mathematically-grounded deep architectures
Convergence and stability proofs for DL models
Generalization bounds for medical imaging models
Geometry of neural networks and kernel methods
Pillar 3

Explainable & Trustworthy AI

Making AI transparent and interpretable using mathematical tools — differential geometry, spectral theory, and information geometry.

Spectral graph theory for model interpretability
Information geometry for understanding neural networks
Model cards and reproducibility standards
Auditable and deployable AI systems
Pillar 4

Real-World Applications: Medical & Energy AI

Applying mathematical AI to real problems — medical imaging diagnosis, renewable energy systems, and smart grid optimization.

Glaucoma detection from retinal fundus images
Bone mineral density prediction from MRI/CT/X-ray
Diabetic retinopathy recognition
Wind turbine control and solar energy optimization
Smart grid and microgrid system analysis

Application Domains

Real-World Impact Areas

Medical Imaging AI

Glaucoma detection, diabetic retinopathy, bone density prediction from MRI/CT/X-ray

Renewable Energy

Wind turbine control systems, solar energy optimization, microgrid development

Smart Grid Systems

Automatic control systems, generator monitoring, energy management platforms

Healthcare Analytics

Brain data analysis, neurological disease assessment, health prediction models

Keywords

Mathematical ModelingOptimizationMachine LearningArtificial IntelligenceDeep LearningMathematical ProgrammingNumerical AnalysisExplainable ModelsBig DataSensitivity AnalysisTheory-based Machine Learning