Custom PDE
2D Sparse Observation Inverse PINN
Enter observations at five fixed locations to identify coefficient a and predict the 2D scalar field, with analytic comparison for the submitted observations.
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 inverse PINN
Identify coefficient a and predict a two-dimensional scalar field from five fixed-location observations.
All five observations must describe the same noiseless condition, with equal observation-to-x ratios. Registered ranges are checked and every prediction is compared with the analytic coefficient and field.
- Geometry
- 2D inverse unit square
- Geometry scope
- same_geometry_only
Adjustable inputs
| Input | Range | Default |
|---|---|---|
| Observation at (0.2, 0.25) | 0.06666666666666667 – 0.2 model unit | 0.1 |
| Observation at (0.4, 0.5) | 0.13333333333333333 – 0.4 model unit | 0.2 |
| Observation at (0.6, 0.75) | 0.19999999999999998 – 0.6 model unit | 0.3 |
| Observation at (0.8, 0.25) | 0.26666666666666666 – 0.8 model unit | 0.4 |
| Observation at (0.9, 0.75) | 0.3 – 0.9 model unit | 0.45 |
Output fields
- PINN scalar field: u
Registered verification
- registered_status
- passed
- thresholds
- coefficient_relative_error: 0.01; field_relative_l2: 0.01; field_max_absolute_error: 0.01
- summary
- 33 noiseless compatible observation scenarios passed coefficient and field checks, including six reserved holdouts.
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.