APDTFlow: Production-Ready Time Series Forecasting with Neural ODEs

The only Python package offering continuous-time forecasting with Neural ODEs. Combine cutting-edge research with a simple fit()/predict() API for production-ready forecasting.

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🎯 What You Can Do with APDTFlow

Get 95% Confidence Intervals in 5 Lines

from apdtflow import APDTFlowForecaster

model = APDTFlowForecaster(forecast_horizon=7, use_conformal=True)
model.fit(df, target_col='sales', date_col='date')
lower, pred, upper = model.predict(alpha=0.05, return_intervals='conformal')
# Output: Guaranteed 95% coverage - perfect for production risk management

Boost Accuracy 30-50% with External Features

model = APDTFlowForecaster(forecast_horizon=14, exog_fusion_type='gated')
model.fit(df, target_col='sales', exog_cols=['temperature', 'holiday', 'promotion'])
predictions = model.predict(exog_future=future_df)
# Output: Seamlessly incorporate weather, holidays, and promotions for better forecasts

Validate Models with Rolling Window Backtesting

results = model.historical_forecasts(data=df, start=0.8, stride=7)
print(f"MASE: {results['abs_error'].mean():.2f}")
# Output: MASE: 0.85 (beats naive forecast! < 1.0 = good)

Handle Irregular Time Series with Neural ODEs

model = APDTFlowForecaster(model_type='ode')  # Continuous-time modeling
model.fit(irregular_data)  # Works with missing data & irregular intervals
predictions = model.predict()
# Output: Neural ODEs handle gaps and irregular sampling naturally

Use Categorical Features (Day-of-Week, Holidays, Store IDs)

model = APDTFlowForecaster(forecast_horizon=7)
model.fit(
    df,
    target_col='sales',
    categorical_cols=['day_of_week', 'store_id', 'promotion_type']
)
predictions = model.predict()
# Output: Automatic one-hot encoding or embeddings - no manual preprocessing needed

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📦 Installation

APDTFlow is published on PyPI:

pip install apdtflow

For development:

git clone https://github.com/yotambraun/APDTFlow.git
cd APDTFlow
pip install -e .

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📑 Table of Contents

1. What You Can Do
2. Installation
3. Why APDTFlow?
4. Key Features
5. Quick Start
6. Features & Usage
7. Model Architectures
8. Evaluation & Metrics
9. Experiment Results
10. Documentation & Examples
11. Additional Capabilities
12. License

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🔬 Why APDTFlow?

Unique Capabilities

APDTFlow stands out with continuous-time forecasting using Neural ODEs and modern research features:

• 🔬 Continuous-Time Neural ODEs: Model temporal dynamics with differential equations - better for irregular time series and missing data
• 📊 Conformal Prediction: Rigorous uncertainty quantification with finite-sample coverage guarantees
• 🌟 Advanced Exogenous Support: 3 fusion strategies (gated, attention, concat) → 30-50% accuracy boost
• 📈 Industry-Standard Metrics: MASE, sMAPE, CRPS, Coverage for rigorous evaluation
• 🔄 Backtesting: Darts-style rolling window validation with historical_forecasts()
• ⚡ Simple API: Just fit() and predict() with multiple architectures (ODE, Transformer, TCN, Ensemble)

When to Use APDTFlow

• Financial forecasting - Rigorous uncertainty bounds for risk management
• Retail demand - Holidays, promotions, seasonal patterns with categorical features
• Energy consumption - Weather, temperature, and external events as exogenous variables
• Healthcare demand - Demographic and policy changes with conformal prediction
• Any scenario requiring continuous-time modeling or sophisticated exogenous variable handling

Comparison with Other Libraries

Feature	APDTFlow	Darts	NeuralForecast	Prophet
Neural ODEs	✅ Continuous-time	❌ No	❌ No	❌ No
Exogenous Variables	✅ 3 fusion strategies	✅ Yes	✅ Yes	✅ Yes
Conformal Prediction	✅ Rigorous uncertainty	⚠️ Limited	❌ No	❌ No
Backtesting	✅ historical_forecasts()	✅ Yes	⚠️ Limited	❌ No
Industry Metrics	✅ MASE, sMAPE, CRPS	✅ Yes	✅ Yes	⚠️ Limited
Categorical Features	✅ One-hot & embeddings	✅ Yes	✅ Yes	⚠️ Limited
Multi-Scale Decomposition	✅ Trends + seasonality	⚠️ Limited	❌ No	✅ Yes
Simple fit()/predict() API	✅ 5 lines of code	✅ Yes	⚠️ Varies	✅ Yes
Multiple Architectures	✅ ODE/Transformer/TCN	✅ Many	✅ Many	❌ One
PyTorch-based	✅ GPU acceleration	⚠️ Mixed	✅ Yes	❌ No

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✨ Key Features

📊 Industry-Standard Metrics

Evaluate with metrics used by leading forecasting teams:

from apdtflow import APDTFlowForecaster

model = APDTFlowForecaster(forecast_horizon=14)
model.fit(df, target_col='sales', date_col='date')

# Industry-standard metrics: MASE, sMAPE, CRPS, Coverage
mase = model.score(test_df, target_col='sales', metric='mase')
# Output: 0.85  # < 1.0 = beats naive forecast

smape = model.score(test_df, target_col='sales', metric='smape')
# Output: 12.3  # Symmetric MAPE percentage

Available Metrics:

• MASE (Mean Absolute Scaled Error) - Scale-independent, M-competition standard
• sMAPE (Symmetric MAPE) - Better than MAPE, bounded 0-200%
• CRPS (Continuous Ranked Probability Score) - For probabilistic forecasts
• Coverage - Prediction interval calibration (e.g., 95% intervals)

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🔄 Backtesting / Historical Forecasts

Validate models with Darts-style rolling window backtesting:

# Backtest model on historical data
backtest_results = model.historical_forecasts(
    data=df,
    target_col='sales',
    date_col='date',
    start=0.8,           # Start at 80% of data
    forecast_horizon=7,  # 7-day forecasts
    stride=7,            # Weekly frequency
    retrain=False,       # Fast: use fixed model
    metrics=['MAE', 'MASE', 'sMAPE']
)

# Output: DataFrame with columns:
#   timestamp, fold, forecast_step, actual, predicted, error, abs_error

print(f"Total forecasts: {backtest_results['fold'].nunique()}")
# Output: Total forecasts: 5

print(f"Average MASE: {backtest_results['abs_error'].mean():.3f}")
# Output: Average MASE: 0.923

Features:

• Rolling window validation - Simulate production forecasting
• Fixed or retrain modes - Trade speed vs realism
• Flexible parameters - Control start point, stride, horizon
• Comprehensive output - Timestamp, actual, predicted, fold, errors

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📊 Conformal Prediction

Get calibrated prediction intervals with coverage guarantees:

model = APDTFlowForecaster(
    forecast_horizon=14,
    use_conformal=True,        # Enable conformal prediction
    conformal_method='adaptive' # Adapts to changing data
)

model.fit(df, target_col='sales')

# Get calibrated 95% prediction intervals
lower, pred, upper = model.predict(
    alpha=0.05,  # 95% coverage guarantee
    return_intervals='conformal'
)

# Output:
#   lower: array([98.2, 97.5, ...])   # Lower bounds
#   pred:  array([105.3, 104.1, ...])  # Point predictions
#   upper: array([112.4, 110.7, ...])  # Upper bounds
# Guarantee: 95% of actual values will fall within [lower, upper]

Why Conformal Prediction?

• Finite-sample guarantees - Not just asymptotic
• Distribution-free - No assumptions about data distribution
• Adaptive methods - Adjust to changing patterns
• Production-ready - Used in finance, healthcare, energy

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🌟 Exogenous Variables

Boost accuracy 30-50% with external features:

# Use external features like temperature, holidays, promotions
model = APDTFlowForecaster(
    forecast_horizon=14,
    exog_fusion_type='gated'  # or 'attention', 'concat'
)

model.fit(
    df,
    target_col='sales',
    date_col='date',
    exog_cols=['temperature', 'is_holiday', 'promotion'],
    future_exog_cols=['is_holiday', 'promotion']  # Known in advance
)

# Predict with future exogenous data
future_exog = pd.DataFrame({
    'is_holiday': [0, 1, 0, 0, ...],
    'promotion': [1, 0, 1, 0, ...]
})
predictions = model.predict(exog_future=future_exog)
# Output: array([135.2, 145.8, 132.1, ...])  # Improved accuracy with external features

Fusion Strategies:

• Gated - Learn importance weights for each feature
• Attention - Dynamic feature weighting based on context
• Concat - Simple concatenation (baseline)

Impact: Research shows 30-50% accuracy improvement in retail, energy, and demand forecasting.

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⚡ Simple API

Production-ready forecasting in 5 lines:

from apdtflow import APDTFlowForecaster

model = APDTFlowForecaster(forecast_horizon=14)
model.fit(df, target_col='sales', date_col='date')
predictions = model.predict()
# Output: array([120.5, 118.3, 122.1, ...])  # 14 predictions

Features:

• Simple fit()/predict() interface - No DataLoaders or manual preprocessing
• Works with pandas DataFrames - Natural integration with your workflow
• Automatic normalization - Just pass your data and go
• Built-in visualization - plot_forecast() with uncertainty bands
• Multiple model types - Switch architectures with one parameter

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🚀 Quick Start

5-Line Forecast

from apdtflow import APDTFlowForecaster

model = APDTFlowForecaster(forecast_horizon=7)
model.fit(df, target_col='sales', date_col='date')
predictions = model.predict()
# Output: array([120.5, 118.3, 122.1, 119.8, 121.2, 123.4, 120.9])

model.plot_forecast(with_history=100)
# Output: [displays matplotlib plot with history and predictions]

Complete Example with Uncertainty

import pandas as pd
from apdtflow import APDTFlowForecaster

# Load your time series data
df = pd.read_csv("dataset_examples/Electric_Production.csv", parse_dates=['DATE'])

# Create and train the forecaster
model = APDTFlowForecaster(
    forecast_horizon=14,     # Predict 14 steps ahead
    history_length=30,       # Use 30 historical points
    num_epochs=50           # Training epochs
)

# Fit the model (handles preprocessing automatically)
model.fit(df, target_col='IPG2211A2N', date_col='DATE')

# Make predictions with uncertainty estimates
predictions, uncertainty = model.predict(return_uncertainty=True)
# Output:
#   predictions: array([95.3, 96.1, 94.8, ...])  # 14 values
#   uncertainty: array([2.1, 2.3, 2.4, ...])     # Standard deviations

# Visualize the forecast
model.plot_forecast(with_history=100, show_uncertainty=True)

Try Different Models

# Use Transformer instead of Neural ODE
model = APDTFlowForecaster(model_type='transformer', forecast_horizon=14)

# Or Temporal Convolutional Network
model = APDTFlowForecaster(model_type='tcn', forecast_horizon=14)

# Or Ensemble for maximum robustness
model = APDTFlowForecaster(model_type='ensemble', forecast_horizon=14)

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🎯 Features & Usage

Advanced API for Custom Workflows

For advanced users who need more control over the training process:

import torch
from torch.utils.data import DataLoader
from apdtflow.data import TimeSeriesWindowDataset
from apdtflow.models.apdtflow import APDTFlow

# Create dataset and dataloader
csv_file = "dataset_examples/Electric_Production.csv"
dataset = TimeSeriesWindowDataset(
    csv_file,
    date_col="DATE",
    value_col="IPG2211A2N",
    T_in=12,  # Input sequence length
    T_out=3   # Forecast horizon
)
train_loader = DataLoader(dataset, batch_size=16, shuffle=True)

# Initialize model
model = APDTFlow(
    num_scales=3,
    input_channels=1,
    filter_size=5,
    hidden_dim=16,
    output_dim=1,
    forecast_horizon=3,
    use_embedding=True
)

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
model.to(device)

# Train
model.train_model(
    train_loader=train_loader,
    num_epochs=15,
    learning_rate=0.001,
    device=device
)

# Evaluate
test_loader = DataLoader(test_dataset, batch_size=16, shuffle=False)
metrics = model.evaluate(test_loader, device, metrics=["MSE", "MAE", "RMSE", "MAPE"])
# Output: {'MSE': 0.234, 'MAE': 0.412, 'RMSE': 0.484, 'MAPE': 4.23}

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🏗️ Model Architectures

APDTFlow includes multiple advanced forecasting architectures:

APDTFlow (Neural ODE)

The APDTFlow model integrates:

• Multi-Scale Decomposition: Decomposes signals into multiple resolutions
• Neural ODE Dynamics: Models continuous latent state evolution
• Probabilistic Fusion: Merges representations while quantifying uncertainty
• Transformer-Based Decoding: Generates forecasts with time-aware attention

Key Parameters:

• T_in: Input sequence length (e.g., 12 = use 12 historical points)
• T_out: Forecast horizon (e.g., 3 = predict 3 steps ahead)
• num_scales: Number of decomposition scales for multi-resolution analysis
• filter_size: Convolutional filter size affecting receptive field
• hidden_dim: Hidden state size controlling model capacity
• forecast_horizon: Must match T_out for consistency

TransformerForecaster

Leverages Transformer architecture with self-attention to capture long-range dependencies. Ideal for complex temporal patterns requiring broad context.

TCNForecaster

Based on Temporal Convolutional Networks with dilated convolutions and residual connections. Efficiently captures local and medium-range dependencies.

EnsembleForecaster

Combines predictions from multiple models (APDTFlow, Transformer, TCN) using weighted averaging for improved robustness and accuracy.

📖 Learn More: Model Architectures Documentation

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📊 Evaluation & Metrics

APDTFlow supports comprehensive evaluation with industry-standard forecasting metrics:

Standard Metrics

• MSE (Mean Squared Error)
• MAE (Mean Absolute Error)
• RMSE (Root Mean Squared Error)
• MAPE (Mean Absolute Percentage Error)

Industry-Standard Metrics

• MASE (Mean Absolute Scaled Error) - Scale-independent, M-competition standard. Values < 1 = beats naive forecast
• sMAPE (Symmetric MAPE) - Symmetric, bounded 0-200%, better than MAPE
• CRPS (Continuous Ranked Probability Score) - Evaluates probabilistic forecasts
• Coverage - Prediction interval calibration (e.g., 95% intervals should contain 95% of actuals)

Usage Example

from apdtflow import APDTFlowForecaster
from apdtflow.evaluation.regression_evaluator import RegressionEvaluator

# High-level API
model = APDTFlowForecaster(forecast_horizon=14)
model.fit(train_df, target_col='sales', date_col='date')

# Score with new metrics
mase = model.score(test_df, target_col='sales', metric='mase')
smape = model.score(test_df, target_col='sales', metric='smape')

print(f"MASE: {mase:.3f} (< 1.0 = beats naive forecast)")
# Output: MASE: 0.850 (< 1.0 = beats naive forecast)

print(f"sMAPE: {smape:.2f}%")
# Output: sMAPE: 12.34%

# Using evaluator directly
evaluator = RegressionEvaluator(metrics=["MSE", "MAE", "MASE", "sMAPE"])
results = evaluator.evaluate(predictions, targets)
print("Metrics:", results)
# Output: Metrics: {'MSE': 0.234, 'MAE': 0.412, 'MASE': 0.850, 'sMAPE': 12.34}

# For probabilistic forecasts with intervals
evaluator_prob = RegressionEvaluator(metrics=["CRPS", "Coverage"])
results_prob = evaluator_prob.evaluate(predictions, targets, lower=lower_bounds, upper=upper_bounds)
print("CRPS:", results_prob["CRPS"], "Coverage:", results_prob["Coverage"])
# Output: CRPS: 1.23 Coverage: 94.5

Backtesting for Robust Validation

# Backtest on historical data
backtest_results = model.historical_forecasts(
    data=df,
    target_col='sales',
    date_col='date',
    start=0.7,           # Start at 70% of data
    forecast_horizon=14,
    stride=14,           # Forecast every 2 weeks
    retrain=False,       # Use fixed model for speed
    metrics=['MAE', 'MASE', 'sMAPE']
)

# Analyze results
print(f"Total forecasts: {backtest_results['fold'].nunique()}")
# Output: Total forecasts: 8

print(f"Average MASE: {backtest_results['abs_error'].mean():.3f}")
# Output: Average MASE: 0.923

# Visualize backtest
import matplotlib.pyplot as plt
plt.figure(figsize=(12, 6))
plt.plot(backtest_results['timestamp'], backtest_results['actual'], 'o-', label='Actual', alpha=0.7)
plt.plot(backtest_results['timestamp'], backtest_results['predicted'], 's-', label='Predicted', alpha=0.7)
plt.legend()
plt.show()

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🧪 Experiment Results

We compared multiple forecasting models across different forecast horizons using 3-fold cross-validation:

Validation Loss Comparison

Key Finding: APDTFlow consistently achieves lower validation losses, especially for longer forecast horizons. Multi-scale decomposition and Neural ODE dynamics effectively capture trends and seasonal patterns.

Performance vs. Forecast Horizon

Analysis: APDTFlow maintains robust performance as forecast horizon increases, demonstrating superior extrapolation capabilities compared to discrete-time models.

Example Forecast (Horizon 7, CV Split 3)

• Blue: Historical input sequence (30 time steps)
• Orange (Dashed): Actual future values
• Dotted Line: APDTFlow predictions

📊 Full Analysis: See Experiment Results Documentation for detailed metrics, ablation studies, and cross-validation analysis.

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📚 Documentation & Examples

Documentation

• User Guide - Comprehensive overview and tutorials
• Model Architectures - Technical details and parameters
• Experiment Results - Benchmarks and analysis
• Configuration Guide - YAML configuration options

Examples

• Backtesting Demo - 5 comprehensive examples: basic backtesting, retrain modes, horizon comparison, visualization, exogenous features
• Categorical Features Demo - Day-of-week, holidays, and categorical variable encoding
• Exogenous Features Demo - External variables (temperature, promotions) with 3 fusion strategies
• Conformal Prediction Demo - Rigorous uncertainty quantification with coverage guarantees

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🛠️ Additional Capabilities

Data Processing & Augmentation

APDTFlow provides robust preprocessing:

• Date Conversion: Automatic datetime parsing
• Gap Filling: Reindexing for consistent time frequency
• Missing Value Imputation: Forward-fill, backward-fill, mean, interpolation
• Feature Engineering: Lag features and rolling statistics
• Data Augmentation: Jittering, scaling, time warping for robustness

Command-Line Interface

Train and infer directly from terminal:

# Train a model
apdtflow train --csv_file path/to/dataset.csv --date_col DATE --value_col VALUE \
  --T_in 12 --T_out 3 --num_epochs 15 --checkpoint_dir ./checkpoints

# Run inference
apdtflow infer --csv_file path/to/dataset.csv --date_col DATE --value_col VALUE \
  --T_in 12 --T_out 3 --checkpoint_path ./checkpoints/APDTFlow_checkpoint.pt

Available Commands:

• apdtflow train - Train a forecasting model
• apdtflow infer - Run inference with saved checkpoint

Cross-Validation Strategies

Robust time series cross-validation:

• Rolling Splits: Moving training and validation windows
• Expanding Splits: Increasing training window size
• Blocked Splits: Contiguous block divisions

from apdtflow.cv_factory import TimeSeriesCVFactory

cv_factory = TimeSeriesCVFactory(
    dataset,
    method="rolling",
    train_size=40,
    val_size=10,
    step_size=10
)
splits = cv_factory.get_splits()
# Output: [(train_indices, val_indices), ...]

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📄 License

APDTFlow is licensed under the MIT License. See LICENSE file for details.

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