Recorded by commits b1525c8 and 4fb1581
Experiment Note
A hard-boundary streamfunction-pressure cavity formulation was introduced and then stabilized. This was retained as a shared physics module, not as a hidden VARA-only improvement.
Technical Essay
The earlier direct-velocity hard-boundary wrapper could satisfy wall velocity while still allowing large interior divergence. A streamfunction-pressure output enforces u = psi_y and v = -psi_x, making continuity exact up to autodifferentiation and floating-point behavior. A boundary-admissible ansatz regularized the lid corners and encoded the wall conditions.
This came at a real cost: the momentum residual now differentiates velocities that are already derivatives of psi, requiring third-order derivatives of the network. Runtime and memory were therefore materially different. The final protocol required this formulation to be reported separately and applied to all compared methods in a formulation study.
Reading Note
Hard-constraint PINN research supports embedding known boundary structure in the trial function. Streamfunction formulations support exact incompressibility in two dimensions. The reading caution was that exact enforcement of one law can increase derivative stiffness or make another objective harder; a stronger inductive bias is not free.
Progress Update
The repository now separated three layers cleanly: core controller, optional shared physics formulation, and continuation. This separation became central to the paper's novelty and fairness claims.