Integration of physics-based models with machine learning techniques, including Physics-Informed Neural Networks (PINNs) for solving differential equations and discovering governing laws from data. Wavelet-based machine learning techniques for solving PDEs.
Recent publications: Wavelet-based PINNs, Fractional machine intelligence frameworks
Advanced algorithms for multiway data analysis, tensor decompositions (CP, Tucker, M-QR), generalized inverses of tensors, and efficient computational methods for high-dimensional data.
40+ publications on tensor inverses, M-QDR decomposition, t-product based methods
Adaptive recurrent neural networks for solving time-varying equations, zeroing neural networks (ZNN), and finite-time neural networks for computational mathematics applications.
Focus on varying-parameter RNNs, robust noise-tolerant networks
High-performance algorithms for large-scale matrix computations, iterative methods for linear systems, eigenvalue problems, and parallel computational techniques.
Specialization in theory and computation of generalized inverses, matrix decomposition methods
Quantum algorithms for numerical linear algebra problems, quantum-based machine learning techniques for solving PDEs.
Emerging research area with focus on quantum tensor networks
