Feature engineering constructs input variables that expose patterns or context missing from raw measurements. A sensor reading may report 185°C; deviation from an optimal temperature, rate of change, and time above a safe range give that reading operational meaning. Unlike an embedding, which encodes similarity in a dense vector, an engineered feature can describe a specific, interpretable relationship. section 4.1.5
Start with clean, normalized data synchronized to a common time grid. Then choose transformations that reflect how the physical system behaves and what the prediction needs to capture. section 8.1.3
For a home digital twin, three useful feature types are:
- Temporal features: encode hour of day as sine and cosine values so 23:00 and 00:00 remain close, rather than appearing at opposite ends of a 0–23 scale. section 8.1.3
- Lagged features: shift earlier indoor temperatures into the current row to expose the previous three hours of temperature change and the building’s thermal memory. section 8.1.3
- Domain-specific features: subtract outdoor temperature from indoor temperature to represent a temperature difference that neither reading expresses alone. section 8.1.3
Listing 8.2 Cyclical encoding of time
import numpy as np
import pandas as pd
df = pd.DataFrame({"hour": range(24)})
df["hour_sin"] = np.sin(2 * np.pi * df["hour"] / 24)
df["hour_cos"] = np.cos(2 * np.pi * df["hour"] / 24)
The NumPy and pandas listing creates two columns for hour of day. Together, the sine and cosine values represent time on a cycle. section 8.1.3
Listing 8.3 Calculating short-term temperature lag features
import pandas as pd
data = {"indoor_temp": [20.0, 20.5, 21.0, 21.5, 22.0, 22.5, 23.0, 23.5,
24.0, 24.5]}
df = pd.DataFrame(data)
df["indoor_temp_lag_1"] = df["indoor_temp"].shift(1)
df["indoor_temp_lag_2"] = df["indoor_temp"].shift(2)
df["indoor_temp_lag_3"] = df["indoor_temp"].shift(3)
df = df.dropna()
print(
df[["indoor_temp", "indoor_temp_lag_1", "indoor_temp_lag_2",
"indoor_temp_lag_3"]]
)
The pandas listing uses shift(1), shift(2), and shift(3) to add prior temperatures, then drops rows without a complete three-hour history. section 8.1.3
Temperature difference as a feature
At midnight, an indoor reading of 22.1°C and an outdoor reading of 8.2°C produce a 13.9°C temperature delta. Calculate the same difference for each synchronized row to give a model an explicit measure of the indoor–outdoor relationship. section 8.1.3
Feature stores such as Hopsworks and Feast can centralize engineered variables, maintain training–serving consistency, and provide versioning, lineage, and low-latency access. AutoML libraries such as FLAML, AutoKeras, and AutoGluon can automate feature engineering alongside model selection and parameter tuning; they offer an alternative to explicitly constructing every feature by hand. section 4.3.6 section 8.3.2
