# A deep generative model for probabilistic energy forecasting in power systems: normalizing flows

arXiv: https://arxiv.org/abs/2106.09370 · HTML: https://mlsanity.com/paper/2106.09370/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 76 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [An empirical study on evaluation metrics of generative adversarial networks](https://mlsanity.com/paper/1806.07755/) (2018)
- [Towards Deeper Understanding of Variational Autoencoding Models](https://mlsanity.com/paper/1702.08658/) (2017)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Complete parameter inference for GW150914 using deep learning](https://mlsanity.com/paper/2008.03312/) (2020)
- [Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks](https://mlsanity.com/paper/1805.06649/) (2018)
- [Bayesian Renewables Scenario Generation via Deep Generative Networks](https://mlsanity.com/paper/1802.00868/) (2018)
- [Probabilistic Energy Forecasting using Quantile Regressions based on a new Nearest Neighbors Quantile Filter](https://mlsanity.com/paper/1903.07390/) (2019)
- [A Probabilistic Forecast-Driven Strategy for a Risk-Aware Participation in the Capacity Firming Market: extended version](https://mlsanity.com/paper/2105.13801/) (2021)
- [Deep learning-based multi-output quantile forecasting of PV generation](https://mlsanity.com/paper/2106.01271/) (2021)

## Built on by (most cited first, 18 of 18)

- [Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows](https://mlsanity.com/paper/2205.13826/) (2022)
- [Risk-Aware Control and Optimization for High-Renewable Power Grids](https://mlsanity.com/paper/2204.00950/) (2022)
- [Continuous and Distribution-free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach](https://mlsanity.com/paper/2206.02433/) (2022)
- [Denoising diffusion probabilistic models for probabilistic energy forecasting](https://mlsanity.com/paper/2212.02977/) (2022)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Generating Synthetic Net Load Data with Physics-informed Diffusion Model](https://mlsanity.com/paper/2406.01913/) (2024)
- [Generative Modeling of Microweather Wind Velocities for Urban Air Mobility](https://mlsanity.com/paper/2503.02690/) (2025)
- [Normalizing Flow-based Day-Ahead Wind Power Scenario Generation for Profitable and Reliable Delivery Commitments by Wind Farm Operators](https://mlsanity.com/paper/2204.02242/) (2022)
- [Sample-based Uncertainty Quantification with a Single Deterministic Neural Network](https://mlsanity.com/paper/2209.08418/) (2022)
- [Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.02168/) (2024)
- [One Model to Forecast Them All and in Entity Distributions Bind Them](https://mlsanity.com/paper/2501.15499/) (2025)
- [Aligning the Evaluation of Probabilistic Predictions with Downstream Value](https://mlsanity.com/paper/2508.18251/) (2025)
- [Time to Market Reduction for Hydrogen Fuel Cell Stacks using Generative Adversarial Networks](https://mlsanity.com/paper/2212.11733/) (2022)
- [Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks](https://mlsanity.com/paper/2302.01800/) (2023)
- [Deep Generative Methods for Producing Forecast Trajectories in Power Systems](https://mlsanity.com/paper/2309.15137/) (2023)
- [Analysis and Applications of Deep Learning with Finite Samples in Full Life-Cycle Intelligence of Nuclear Power Generation](https://mlsanity.com/paper/2311.04247/) (2023)
- [AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability](https://mlsanity.com/paper/2412.00419/) (2024)
- [Ensemble Complexity in Photovoltaic Forecasting](https://mlsanity.com/paper/2609.15049/) (2026)

## Abstract (arXiv)

Greater direct electrification of end-use sectors with a higher share of renewables is one of the pillars to power a carbon-neutral society by 2050. However, in contrast to conventional power plants, renewable energy is subject to uncertainty raising challenges for their interaction with power systems. Scenario-based probabilistic forecasting models have become a vital tool to equip decision-makers. This paper presents to the power systems forecasting practitioners a recent deep learning technique, the normalizing flows, to produce accurate scenario-based probabilistic forecasts that are crucial to face the new challenges in power systems applications. The strength of this technique is to directly learn the stochastic multivariate distribution of the underlying process by maximizing the likelihood. Through comprehensive empirical evaluations using the open data of the Global Energy Forecasting Competition 2014, we demonstrate that this methodology is competitive with other state-of-the-art deep learning generative models: generative adversarial networks and variational autoencoders. The models producing weather-based wind, solar power, and load scenarios are properly compared in terms of forecast value by considering the case study of an energy retailer and quality using several complementary metrics. The numerical experiments are simple and easily reproducible. Thus, we hope it will encourage other forecasting practitioners to test and use normalizing flows in power system applications such as bidding on electricity markets, scheduling power systems with high renewable energy sources penetration, energy management of virtual power plan or microgrids, and unit commitment.