12 papers
LiNO: Lifting based multiresolution neural operator
Himanshu Pandey, Subham Patel, Ratikanta Behera
Recently, neural operators have shown promising outcomes for learning solution operators of differential equations directly from data. This framework learns a functional mapping fr…
Quantum Physics-Informed Neural Networks for Solving Integro and Fractional PDEs
Deepak Gupta, Ratikanta Behera
Quantum neural networks have emerged as powerful models for approximating nonlinear functions. Yet their use in solving integro-differential equations (IDEs) and fractional integro…
Quaternion Nonlinear Transform-Induced Nuclear Norm for Low-Rank Tensor Completion
Biswarup Karmakar, Ratikanta Behera
Tensor completion has emerged as a powerful framework for recovering missing data in multidimensional signals by exploiting low-rank tensor structures. Among existing approaches, l…
A Family of Iterative Methods for Computing Generalized Inverses of Quaternion Matrices and its Applications
Biswarup Karmakar, Neha Bhadala, Ratikanta Behera
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image res…
An adaptive wavelet-based PINN for problems with localized high-magnitude source
Himanshu Pandey, Ratikanta Behera
In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitation…
Structure Preserving Algorithms for Quaternion Outer Inverses with Applications
Neha Bhadala, Ratikanta Behera
This study investigates the theoretical and computational aspects of quaternion generalized inverses, focusing on outer inverses and {1,2}-inverses with prescribed range and/or nul…