Take Home MessagesðŠķ
- Replicating your results with a separate training loop helps reveal any bugs that are masked by expected results.
- Don't carelessly introduce normalization steps without keeping track. If you make the decision to double-normalize, have a justification and make a note of it.
Rule of Thumb
Normalize the Domain, Constrain the Range
Project 2 Normalization Steps
| Step | Method | Type | Justification |
|---|---|---|---|
| 1. Grid Setup | make_grid |
Domain | Prevents "stiff" gradients originating from extreme input scales |
| 2. Wavefunction Normalization | NormalizedWavefunctionNet |
Range | Guarantees physical probability density = 1. |
| 3. Orthonormality | Gram-Schmidt | Range | Prevents mode collapse; ensures unique eigenstates |
| 4. Stability | \(\epsilon=1e-8\) | Range | Prevents NaN during initialization |
| 5. Sign Correction | Overlap check | Alignment | Resolves \(\pm \psi_n^\theta(x)\) phase ambiguity for plotting |
| 6. POD Scaling | \(1/\sqrt{dx}\) | Alignment | Maps abstract SVD vectors to physical L2 norms |