3 papers
math.OC2026
Distributed optimal control problems governed by poroelasticity equations
Arbaz Khan, Jeonghun J. Lee, Harpal Singh
In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poro…
math.NA2026
Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
Shiv Mishra, Arbaz Khan
We develop a new class of physics-informed neural network approximations for the stationary Oseen equations based on stability-consistent loss constructions. In contrast to standar…
math.NA2026
Mixed Consistent PINNs for Elliptic Obstacle Problems with Stability Analysis
Arbaz Khan, Kent-Andre Mardal, Shiv Mishra
We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed lo…