# Bayesian Neural Networks for Virtual Flow Metering: An Empirical Study

arXiv: https://arxiv.org/abs/2102.01391 · HTML: https://mlsanity.com/paper/2102.01391/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 12 of 12)

- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Deep Learning: A Bayesian Perspective](https://mlsanity.com/paper/1706.00473/) (2017)
- [Developing a Hybrid Data-Driven, Mechanistic Virtual Flow Meter -- a Case Study](https://mlsanity.com/paper/2002.02737/) (2020)
- [Toward an enhanced Bayesian estimation framework for multiphase flow soft-sensing](https://mlsanity.com/paper/1406.4306/) (2014)

## Built on by (most cited first, 5 of 5)

- [Multi-task learning for virtual flow metering](https://mlsanity.com/paper/2103.08713/) (2021)
- [On gray-box modeling for virtual flow metering](https://mlsanity.com/paper/2103.12513/) (2021)
- [Passive learning to address nonstationarity in virtual flow metering applications](https://mlsanity.com/paper/2202.03236/) (2022)
- [When is gray-box modeling advantageous for virtual flow metering?](https://mlsanity.com/paper/2110.05034/) (2021)
- [Multi-task and few-shot learning in virtual flow metering](https://mlsanity.com/paper/2309.15828/) (2023)

## Abstract (arXiv)

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. Encouraging results and advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). Data-driven VFMs are developed in the small data regime, where it is important to question the uncertainty and robustness of models. The modeling of uncertainty may help to build trust in models, which is a prerequisite for industrial applications. The contribution of this paper is the introduction of a probabilistic VFM based on Bayesian neural networks. Uncertainty in the model and measurements is described, and the paper shows how to perform approximate Bayesian inference using variational inference. The method is studied by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where an average error of 4-6% and 8-13% is achieved for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. Prediction performance and uncertainty calibration is explored in detail and discussed in light of four data challenges. The findings motivate the development of alternative strategies to improve the robustness of data-driven VFMs.