Score the full model against the base model; compile the search step

Validation: the walk-forward evaluator now replays all zones together
with the full model (electrical heat, neighbour exchange, ventilation
and recovery) using the parameters frozen at the forecast start and the
electrical heat and window openings that actually happened, and scores
the base 3-parameter model on the same spans. Forecast Error sensors
add base_model_mae and improvement_vs_base (share of the base model's
error the new features remove; 0 = no gain, negative = worse). Saved
0.3 statistics load with their own error as the base column.

On synthetic apartments, 60-minute error full vs base: gaming office
0.031 vs 0.182 °C (83 % better), bedroom with ventilation 0.026 vs
0.218 °C (88 %), two coupled rooms 0.024 vs 0.037 °C (34 %; gone by
120 min, where the constant-outdoor assumption dominates). The same
ventilation week without window sensors shows no improvement, as it
should. These check the method, not real-world accuracy.

Performance: every term of a zone's 5-minute change is affine in the
zone temperatures and the radiator lag, and which layer applies depends
only on which inputs exist. compile_step_model reads the coefficients
off the real model per zone and step, so the plan search does a few
multiply-adds per step. It matches the direct model to 1e-12 and makes
a 180-minute, 5-zone search 4.5x faster (0.73 s here, close to the old
base-only search).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

custom_components/heating_mpc/sensor.py

@@ -164,13 +164,15 @@ class MPCForecastError(CoordinatorEntity, SensorEntity):
             "bias": accuracy.get("bias"),
             "persistence_mae": accuracy.get("persistence_mae"),
             "skill": accuracy.get("skill"),
+            "base_model_mae": accuracy.get("base_model_mae"),
+            "improvement_vs_base": accuracy.get("improvement_vs_base"),
             # Per zone, by name.
             "zones": {self.coordinator.zones[key].name if key in self.coordinator.zones else key: stats
                       for key, stats in accuracy.get("rooms", {}).items()},
             "window_days": WINDOW_DAYS,
             "unit_of_attributes": "°C",
-            "basis": ("thermal model replayed with the actual relay history; outdoor "
-                      "temperature held at the start value"),
+            "basis": ("all zones replayed together with the actual relay, electrical heat and "
+                      "window history; outdoor temperature held at the start value"),
         }