Custom PDE
2D Poisson PINN with Adjustable Boundaries
Adjust the left and right boundary values on a unit square, predict the 2D scalar field, and compare every point with the analytic solution for the submitted conditions.
Published scope
The inputs, geometry and outputs below follow the registered public case. Published verification applies only to the stated conditions. Service availability requires a live request.
Conditional PINN
Left and right boundary values determine a scalar field on a two-dimensional square, with zero normal derivatives on the other boundaries.
Predict the two-dimensional scalar field for registered boundary values and compare each point with the current analytic solution.
- Geometry
- 2D unit square
- Geometry scope
- same_geometry_only
Adjustable inputs
| Input | Range | Default |
|---|---|---|
| Left boundary value | 0.5 – 1.5 model unit | 1.0 |
| Right boundary value | 0.0 – 0.25 model unit | 0.125 |
Output fields
- PINN scalar field: u
Registered verification
- registered_status
- passed
- thresholds
- max_relative_l2: 0.01; max_absolute_error: 0.01; max_boundary_error: 0.01; max_laplacian_rms: 0.1
- summary
- 27 conditions passed the analytic field checks; every Web request is compared with its analytic solution.
Recorded workflow evidence
- Project opening
- PASS
- Save and reopen
- PASS
- Training
- NOT_RUN
- Prediction
- NOT_RUN
- Independent accuracy
- NOT_RUN
- Portable validation
- NOT_RUN
These are recorded checks; they do not establish live service availability or accuracy for every new request.