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Monotonic Sidecars — Physics Constraints

The Problem

WSPR data contains survivorship bias: during geomagnetic storms (high Kp), only strong signals are decoded. A naive DNN learns "storms = good" — the Kp Inversion Problem.

The Solution: Dual Monotonic Sidecars

Two small MonotonicMLP networks enforce physics constraints that the DNN cannot override:

Sun Sidecar (SFI → SNR boost)

  • Input: Solar Flux Index (SFI), normalized as SFI / 300
  • Constraint: Monotonic increasing — higher SFI always improves SNR
  • Physics: More solar flux → more ionization → better HF propagation

Storm Sidecar (Kp → SNR penalty)

  • Input: kp_penalty = 1 - Kp/9 (inverted so monotonic increasing = storms degrade)
  • Constraint: Monotonic increasing — higher penalty (lower Kp) always improves SNR
  • Physics: Geomagnetic storms → ionospheric disturbance → absorption/fading

Relief Valve Design

Parameter Value Purpose
Weight Clamp Range 0.5 – 2.0 Prevents collapse AND explosion
fc1.bias Frozen Maintains activation shape
fc2.bias Learnable (-10.65) Relief valve for calibration
Initial fc2.bias -10.0 Defibrillator jump-start

Physics Verification

Test Condition Result Grade
Sun Test SFI 70 → 200 +0.482σ (~3.2 dB) PASS
Storm Test Kp 0 → 9 +3.487σ (~23.4 dB) PASS
Polar Storm Kp 2 → 8 (polar) +2.5 dB PASS
D-Layer 80m vs 20m noon +0.0 dB PASS

Training on aggregated signatures shows strong physics response with correct monotonicity.

SFI × Kp Matrix

Reference path: W3 → G (5,900 km, 20m)

SFI \ Kp Kp=0 Kp=2 Kp=5 Kp=9
SFI 70 -20.0 -21.1 -22.0 -24.0
SFI 150 -19.0 -20.0 -21.0 -23.0
SFI 200 -18.0 -19.0 -20.0 -22.0

Down = higher SFI = better. Right = higher Kp = worse. Correct physics.