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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…