3 citations · 5 across the 5 of their papers we have counts for
5 papers
Physics-Informed Neural Network Frameworks for the Analysis of Engineering and Biological Dynamical Systems Governed by Ordinary Differential Equations
Tyrus Whitman, Andrew Particka, Christopher Diers +3
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dyn…
PBPK-iPINNs: Inverse Physics-Informed Neural Networks for Physiologically Based Pharmacokinetic Brain Models
Charuka D. Wickramasinghe, Krishanthi C. Weerasinghe, Pradeep K. Ranaweera +1
Physics-Informed Neural Networks (PINNs) integrate machine learning with differential equations to solve forward and inverse problems while ensuring that predictions adhere to phys…
A Graded Mesh Refinement for 2D Poisson's Equation on Non Convex Polygonal Domains
Charuka D. Wickramasinghe, Priyanka Ahire
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, elect…
A Mixed Finite Element Method for Singularly Perturbed Fourth Oder Convection-Reaction-Diffusion Problems on Shishkin Mesh
Charuka D. Wickramasinghe
This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive paramete…
A finite element method for the biharmonic problem with Dirichlet boundary conditions in a polygonal domain
Hengguang Li, Charuka D. Wickramasinghe, Peimeng Yin
In this paper, we study the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-o…