Research Activities

Research Areas

Scientific Machine Learning

Integration of physics-based models with machine learning techniques to solve complex scientific problems and discover governing equations from data.

  • Physics-Informed Neural Networks (PINNs)
  • Data-Driven Discovery of PDEs
  • Hybrid Physics-ML Models
  • Reduced Order Modeling
  • Multi-Scale Modeling

Tensor Computations and Applications

Advanced algorithms for multiway data analysis in high-dimensional spaces with focus on tensor decompositions and efficient computational methods.

  • Tensor Factorization
  • Tensor Generalized Inverses
  • Tensor-based Iterative Methods
  • Tensor Completion Problems
  • Tensor Neural Networks

Artificial Neural Networks

Adaptive recurrent neural networks for solving time-varying tensor equations and development of specialized architectures for scientific computing.

  • Recurrent Tensor Neural Networks
  • Zeroing Neural Networks (ZNN)
  • Finite-Time Neural Networks
  • Adaptive Neural Architectures
  • Neural ODEs & PDEs

Numerical Linear Algebra

High-performance algorithms for large-scale matrix and tensor computations with development of efficient solvers for scientific computing applications.

  • Iterative Linear System Solvers
  • Matrix Decomposition Methods
  • Eigenvalue & SVD Computations
  • Generalized Inverses and Applications
  • Parallel & HPC Algorithms

Wavelets in Scientific Computing

Adaptive wavelet algorithms for solving PDEs, integral equations, and signal processing problems with focus on fractional-order differential equations.

  • Adaptive Wavelet Collocation Methods
  • Spherical Wavelets
  • Time-Fractional Integro-PDEs
  • Multiresolution Analysis
  • Signal & Image Processing

Quantum Computing

Quantum algorithms for tensor computations and numerical linear algebra with exploration of quantum advantage in high-dimensional scientific computing.

  • Quantum Numerical Linear Algebra
  • Quantum Machine Learning
  • Quantum Tensor Networks
  • Solution of PDEs using Quantum

Demo Applications & Tools

Tensor Calculator

Interactive tool for tensor operations, decompositions, and visualizations with real-time computation.

Launch Demo

Wavelet Analyzer

Advanced wavelet analysis tool for signal processing and solving fractional differential equations.

Launch Demo

Physics-ML Integration

Demonstrate physics-informed machine learning models for solving scientific computing problems.

Launch Demo

Research Statistics

45+
Publications
760+
Citations
10+
Active Members
4+
Research Grants
2+
Open Source Tools