# Continuous and Distribution-free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach

arXiv: https://arxiv.org/abs/2206.02433 · HTML: https://mlsanity.com/paper/2206.02433/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 6 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [Cubic-Spline Flows](https://mlsanity.com/paper/1906.02145/) (2019)
- [Smoothness and Stability in GANs](https://mlsanity.com/paper/2002.04185/) (2020)
- [A deep generative model for probabilistic energy forecasting in power systems: normalizing flows](https://mlsanity.com/paper/2106.09370/) (2021)
- [Optimal Adaptive Prediction Intervals for Electricity Load Forecasting in Distribution Systems via Reinforcement Learning](https://mlsanity.com/paper/2205.08698/) (2022)

## Built on by (most cited first, 7 of 7)

- [WindFM: An Open-Source Foundation Model for Zero-Shot Wind Power Forecasting](https://mlsanity.com/paper/2509.06311/) (2025)
- [Explainable Modeling for Wind Power Forecasting: A Glass-Box Approach with High Accuracy](https://mlsanity.com/paper/2310.18629/) (2023)
- [Improving the Accuracy and Interpretability of Neural Networks for Wind Power Forecasting](https://mlsanity.com/paper/2312.15741/) (2023)
- [Marginalize, Rather than Impute: Probabilistic Wind Power Forecasting with Incomplete Data](https://mlsanity.com/paper/2403.03631/) (2024)
- [A Data-driven Dynamic Temporal Correlation Modeling Framework for Renewable Energy Scenario Generation](https://mlsanity.com/paper/2501.14233/) (2025)
- [Resilient Load Forecasting under Climate Change: Adaptive Conditional Neural Processes for Few-Shot Extreme Load Forecasting](https://mlsanity.com/paper/2602.04609/) (2026)
- [Stabilizing distribution-free probabilistic forecasts](https://mlsanity.com/paper/2605.28531/) (2026)

## Abstract (arXiv)

We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its non-affine characteristics. Over the training phase, the model sequentially maps input examples onto samples of base distribution, given the conditional contexts, where parameters are estimated through maximum likelihood. To issue probabilistic forecasts, one eventually maps samples of the base distribution into samples of a desired distribution. Case studies based on open datasets validate the effectiveness of the proposed model, and allows us to discuss its advantages and caveats with respect to the state of the art.