INITIALIZING REGRESSION CORE...
๐Ÿ“Š

Regression Output

Final Multi-Target Prediction

Inputs
64
Outputs
1
RMSE
19.53
Rยฒ
0.997
โ†’ โ‘  Forward Pass
๐Ÿ“Š โ‘ก Loss Calculation
โ† โ‘ข Backpropagation
โ˜€๏ธ GHI Prediction Output
542
W/mยฒ
Global Horizontal Irradiance
โš–๏ธ Weight Matrix (64โ†’1)
ลท = ฮฃ(wแตขยทxแตข) + b = 542.3
๐Ÿ“ Live Computation
Forward Pass
wโ‚€ยทxโ‚€ =
wโ‚ยทxโ‚ =
wโ‚‚ยทxโ‚‚ =
... (64 total)
โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€
ฮฃ = W/mยฒ
Post-Filter
y_final = max(0, ) = W/mยฒ
Loss Calculation
MSE = (ลท - y_true)ยฒ =
L2 = ฮปยทโ€–Wโ€–ยฒ =
Total =
Gradient (โˆ‚L/โˆ‚wโ‚€)
ฮด = (ลท - y_true) =
โˆ‡wโ‚€ = ฮด ยท xโ‚€ =
๐Ÿ”’ Physics Constraints
๐Ÿ“
Non-Negativity Filter
y_final = max(0, ลท)
โœ…
๐ŸŒก๏ธ
Solar Constant Bound
GHI โ‰ค 1367 W/mยฒ
โœ…
โ˜๏ธ
Clearness Index
KT = 0.82
โœ…
๐ŸŒ…
Solar Zenith
ฮธz = 25.4ยฐ
โšก
๐Ÿ”ฌ Bayesian Optimal Hyperparams
Dropout ฮฑ0.104
L2 Reg ฮป1.2e-4
Learning Rate0.00175
โšก Scenario Injection
โš”๏ธ Complexity Paradox (Table VII)
Model Phys Attn RMSE Rยฒ
Baseline 12F โœ— โœ— 55.32 0.970
Attn-Hybrid 15F โœ“ โœ“ 30.64 0.992
PI-Hybrid 15F โœ“ โœ— 19.53 0.997
๐Ÿ“ˆ 5-Year Stress Test
Regression Equation
ลท = Wยทx + b (Linear)
y_final = max(0, ลท)
KT = GHI/(GHI_cs + 1)
L = MSE + ฮปยทโ€–Wโ€–ยฒ
Epoch
0 / 100
RMSE (W/mยฒ)
25.01
RMSE ฮ”
โ€”
Best RMSE
25.01
Training Progress
EPOCH 0 / 100