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.