Below is a step-by-step guide (with example code) on how you can preprocess a 2-feature time series for predicting the next 10 steps with an LSTM, then build, train, and evaluate the model in TensorFlow/Keras. Adjust window sizes, hyperparameters, etc., as needed for your specific use case.

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1. Imports and data loading

python
import numpy as np
import pandas as pd
from sklearn.preprocessing import MinMaxScaler
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense, Dropout
from tensorflow.keras.optimizers import Adam

python
# Assume you already have:
# data = pd.read_csv('realDataForTrain.csv', skiprows=1, names=['col1', 'col2'])

print(data.info())
print(data.head())

You have two columns:

• col1 in [-100, 100]
• col2 in [0, 100]

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2. Scaling the data

LSTMs often perform better when data is scaled (e.g., between 0 and 1). Because your features have different ranges, a good practice is to scale them using a MinMaxScaler.

python
scaler = MinMaxScaler(feature_range=(0, 1))
scaled_data = scaler.fit_transform(data[['col1', 'col2']])

print(f"Scaled shape: {scaled_data.shape}")
# scaled_data is now a NumPy array with shape (853, 2)

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3. Create sequences (windowing) and labels

We want to predict the next 10 steps given a certain window of prior data (for example, 20 timesteps of history).

• window_size: how many past timesteps we include in a single sample (e.g., 20).
• horizon: how many future timesteps we want to predict (10).

Here is a function that, given a 2D array (scaled_data), builds input sequences (X) and corresponding labels (y).

python
def create_sequences(dataset, window_size=20, horizon=10):
    """
    dataset: scaled dataset of shape (num_samples, num_features)
    window_size: how many past timesteps to include
    horizon: how many future timesteps to predict
    """
    X, y = [], []
    # We stop at len(dataset) - window_size - horizon 
    # so we don't go out of bounds.
    for i in range(len(dataset) - window_size - horizon + 1):
        seq_x = dataset[i : i + window_size]
        seq_y = dataset[i + window_size : i + window_size + horizon]
        X.append(seq_x)
        y.append(seq_y)
        
    return np.array(X), np.array(y)

window_size = 20
horizon = 10

X, y = create_sequences(scaled_data, window_size=window_size, horizon=horizon)

print("X shape:", X.shape)  # (num_samples, window_size, num_features)
print("y shape:", y.shape)  # (num_samples, horizon, num_features)

• X.shape would look like (853 - 20 - 10 + 1, 20, 2) = (824, 20, 2)
• y.shape would look like (824, 10, 2)

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4. Train-Test split

Let’s split our sequences into a train set and a test set. You can also consider having a separate validation set if desired. For simplicity, let’s do an 80%-train / 20%-test split.

python
train_size = int(len(X) * 0.8)

X_train = X[:train_size]
y_train = y[:train_size]

X_test = X[train_size:]
y_test = y[train_size:]

print("Train set:", X_train.shape, y_train.shape)
print("Test set:", X_test.shape, y_test.shape)

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5. Build the LSTM model

We need an LSTM that outputs horizon * num_features values if we want to predict all timesteps at once. Alternatively, we can output (horizon, num_features) by using an LSTM layer with return_sequences=True and additional time-distributed layers.

Below is one approach:

1. Flatten the output so we can predict all future points in one shot: units = horizon * num_features.
2. Reshape the predictions after the model outputs them (if needed).

We’ll create a simple stacked LSTM that outputs horizon * 2 units (because we have 2 features and want 10 timesteps → 10 * 2 = 20 outputs).

python
num_features = X.shape[2]  # should be 2
model = Sequential()
model.add(LSTM(64, return_sequences=False, input_shape=(window_size, num_features)))
model.add(Dropout(0.2))
model.add(Dense(horizon * num_features))  # 10 timesteps * 2 features = 20 outputs

model.compile(loss='mse', optimizer=Adam(learning_rate=0.001), metrics=['mse'])
model.summary()

Note: If you want the model to output a 3D shape directly (i.e., shape (horizon, num_features)), you’d do something more advanced (like return_sequences=True and a TimeDistributed Dense). But for a simpler single Dense output, we flatten to 20 units.

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6. Train (fit) the model

Because our y_train shape is (samples, horizon, num_features), we must reshape it to (samples, horizon * num_features) to match the model’s final Dense(horizon * num_features) layer.

python
y_train_reshaped = y_train.reshape(y_train.shape[0], horizon * num_features)
y_test_reshaped = y_test.reshape(y_test.shape[0], horizon * num_features)

history = model.fit(
    X_train, 
    y_train_reshaped,
    validation_data=(X_test, y_test_reshaped),
    epochs=50,       # Adjust epochs as needed
    batch_size=32,   # Adjust batch_size as needed
    verbose=1
)

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7. Evaluate the model

To evaluate, we can look at the final loss on the test set, or we can get predictions and compare them to actual values. Let’s compute MSE on the test set as reported by model.evaluate, then we’ll also do a direct comparison on the actual predictions.

python
mse_test = model.evaluate(X_test, y_test_reshaped, verbose=0)
print(f"Test MSE: {mse_test[0]:.5f}")

# Get predictions
predictions = model.predict(X_test)
print("Predictions shape:", predictions.shape)
# Reshape predictions back to (samples, horizon, num_features)
predictions = predictions.reshape(predictions.shape[0], horizon, num_features)

# If you'd like to invert the scaling for interpretability:
# 1. Flatten predictions to 2D
predictions_2d = predictions.reshape(-1, num_features)
# 2. Invert scaling
predictions_inverted = scaler.inverse_transform(predictions_2d)
# 3. Reshape back to 3D
predictions_inverted = predictions_inverted.reshape(predictions.shape[0],
                                                    predictions.shape[1],
                                                    predictions.shape[2])

# Do the same for y_test
y_test_2d = y_test.reshape(-1, num_features)
y_test_inverted = scaler.inverse_transform(y_test_2d)
y_test_inverted = y_test_inverted.reshape(y_test.shape[0],
                                          y_test.shape[1],
                                          y_test.shape[2])

print("Predictions (first sample, all 10 timesteps):")
print(predictions_inverted[0])
print("Actual (first sample, all 10 timesteps):")
print(y_test_inverted[0])

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8. Next steps & tips

1. Hyperparameters: Tweak the window_size (history), horizon (forecast steps), units (LSTM cells), learning_rate, batch_size, and epochs for better performance.
2. Validation: Consider adding a separate validation set or using cross-validation to tune hyperparameters.
3. Architectures: Experiment with different network architectures, e.g., multiple LSTM layers (using return_sequences=True on intermediate layers).
4. Loss function: If you need more robust measures, consider MAE, MAPE, or custom metrics.
5. Regularization: Increase or decrease Dropout or add L2 regularization to avoid overfitting if your training set is small.

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Putting it all together

python
import numpy as np
import pandas as pd
from sklearn.preprocessing import MinMaxScaler
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense, Dropout
from tensorflow.keras.optimizers import Adam

# 1. Load data
data = pd.read_csv('realDataForTrain.csv', skiprows=1, names=['col1', 'col2'])

# 2. Scale data
scaler = MinMaxScaler(feature_range=(0, 1))
scaled_data = scaler.fit_transform(data[['col1', 'col2']])

# 3. Create sequences
def create_sequences(dataset, window_size=20, horizon=10):
    X, y = [], []
    for i in range(len(dataset) - window_size - horizon + 1):
        seq_x = dataset[i : i + window_size]
        seq_y = dataset[i + window_size : i + window_size + horizon]
        X.append(seq_x)
        y.append(seq_y)
    return np.array(X), np.array(y)

window_size = 20
horizon = 10
X, y = create_sequences(scaled_data, window_size, horizon)
num_features = X.shape[2]  # should be 2

# 4. Train-Test Split
train_size = int(len(X) * 0.8)
X_train, X_test = X[:train_size], X[train_size:]
y_train, y_test = y[:train_size], y[train_size:]

# 5. Build Model
model = Sequential()
model.add(LSTM(64, return_sequences=False, input_shape=(window_size, num_features)))
model.add(Dropout(0.2))
model.add(Dense(horizon * num_features))  # 10 steps * 2 features = 20

model.compile(loss='mse', optimizer=Adam(learning_rate=0.001), metrics=['mse'])
model.summary()

# 6. Train Model
y_train_reshaped = y_train.reshape(y_train.shape[0], horizon * num_features)
y_test_reshaped = y_test.reshape(y_test.shape[0], horizon * num_features)

history = model.fit(
    X_train,
    y_train_reshaped,
    validation_data=(X_test, y_test_reshaped),
    epochs=50,
    batch_size=32,
    verbose=1
)

# 7. Evaluate
mse_test = model.evaluate(X_test, y_test_reshaped, verbose=0)
print(f"Test MSE: {mse_test[0]:.5f}")

# 8. Predictions and Inverse Transform
pred = model.predict(X_test)
pred = pred.reshape(pred.shape[0], horizon, num_features)

# Invert scale
pred_2d = pred.reshape(-1, num_features)
pred_inverted = scaler.inverse_transform(pred_2d)
pred_inverted = pred_inverted.reshape(pred.shape[0], pred.shape[1], pred.shape[2])

y_test_inverted = scaler.inverse_transform(y_test.reshape(-1, num_features))
y_test_inverted = y_test_inverted.reshape(y_test.shape[0], y_test.shape[1], y_test.shape[2])

print("Predictions (sample 0):")
print(pred_inverted[0])
print("Actual (sample 0):")
print(y_test_inverted[0])

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That’s it! This end-to-end example shows how to:

1. Load and scale data.
2. Create supervised sequences for multi-step forecasting.
3. Build and compile a simple LSTM network.
4. Train, evaluate, and finally invert the scaling to interpret your predictions.

You can adjust hyperparameters (e.g., window_size, horizon, number of LSTM units, learning rate, etc.) to improve performance for your specific dataset.