Input: 2D Manifold Coordinates

Z ∈ ℝ^42×2

42 county-years × 2 dimensions

Manifold Coordinates:

z₁: Metabolic Vigor

z₂: Phenological Timing

Each point's position encodes phenological signature

Regression Model Selection

Corn% = β₀ + β₁·z₁ + β₂·z₂ + ε

Linear relationship on manifold

KNN (k=5)
RMSE: 6.33% | MAE: 4.90%

✓ Linear Regression (Ridge, α=1.0)
RMSE: 5.96% | MAE: 4.60% ⭐ BEST

Polynomial (deg=2)
RMSE: 6.66% | MAE: 5.26%

Gaussian Process
RMSE: 9.42% | MAE: 7.32%

Selected: Ridge Regression

Best RMSE + uniform residuals

Linear model indicates composition varies linearly on 2D manifold

Output: Crop Composition Predictions

RMSE: 5.16%

MAE: 3.64%

R²: 0.712

RMSE: 6.52%

MAE: 5.19%

R²: 0.540

Generalization Gap: 1.36%

Exceptional temporal stability!

Model generalizes across years without retraining