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Take Home MessagesðŸŠķ

  1. Replicating your results with a separate training loop helps reveal any bugs that are masked by expected results.
  2. 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