Score forecasts against reality; expose forecast trajectories

There was no evidence of how accurate the thermal model is: the only
number was an in-sample 5-minute error.

At every poll, record each room's reading, the outdoor temperature, the
radiator-lag estimate and the model parameters. 15, 30, 60 and 120
minutes later, replay the room from that poll with the parameters it
had then (out of sample), the outdoor temperature held constant and the
radiator lag that actually followed from the relay's real history, and
compare with the reading now. A no-change forecast is scored alongside.
Only spans with regular polls and a well-known lag are scored. 7 days
of per-room statistics are saved with the model (optional "evaluation"
payload key; about 18 KB at most).

Four new sensors, Heating MPC Forecast Error 15/30/60/120 min, show the
mean absolute error with bias, persistence error, skill and per-room
detail. On the synthetic lagged plant the 60-minute error is 0.03 °C
against 0.39 °C for persistence.

Room forecast entities gain forecast_15min and plan_15min attributes
and are labelled counterfactual. Volatile attributes are unrecorded.
The model is now saved after scoring, so saved statistics are current.

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

custom_components/heating_mpc/physics.py

@@ -278,10 +278,19 @@ def optimize(
     if result is None:
         raise RuntimeError("No feasible schedule")
     plan, temps_60m, temps_end = result
+    # Re-simulate the chosen plan for its trajectory, keeping the search loop lean.
+    trajectory: dict[str, list[float]] = {room: [] for room in temps}
+    state, lag = dict(temps), effective_heat
+    for bit in plan:
+        for _ in range(nsteps_per_block):
+            state, lag = simulate_step(state, outside, lag, bit, learners)
+        for room, value in state.items():
+            trajectory[room].append(round(value, 3))
     return {
         "proposal": bool(plan[0]),
         "plan_15min": [int(v) for v in plan],
         "predicted_60m": {r: round(t, 3) for r, t in temps_60m.items()},
         "predicted_end": {r: round(t, 3) for r, t in temps_end.items()},
+        "trajectory_15min": trajectory,
         "cost": round(best, 4),
     }