# Passive learning to address nonstationarity in virtual flow metering applications

arXiv: https://arxiv.org/abs/2202.03236 · HTML: https://mlsanity.com/paper/2202.03236/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Tackling Virtual and Real Concept Drifts: An Adaptive Gaussian Mixture Model](https://mlsanity.com/paper/2102.05983/) (2021)
- [Developing a Hybrid Data-Driven, Mechanistic Virtual Flow Meter -- a Case Study](https://mlsanity.com/paper/2002.02737/) (2020)
- [Multi-task learning for virtual flow metering](https://mlsanity.com/paper/2103.08713/) (2021)
- [Bayesian Neural Networks for Virtual Flow Metering: An Empirical Study](https://mlsanity.com/paper/2102.01391/) (2021)
- [On gray-box modeling for virtual flow metering](https://mlsanity.com/paper/2103.12513/) (2021)
- [Identifiability and physical interpretability of hybrid, gray-box models -- a case study](https://mlsanity.com/paper/2010.13416/) (2020)
- [Information theory for non-stationary processes with stationary increments](https://mlsanity.com/paper/1912.03172/) (2019)

## Built on by (most cited first, 3 of 3)

- [Multi-task and few-shot learning in virtual flow metering](https://mlsanity.com/paper/2309.15828/) (2023)
- [Sequential Monte Carlo applied to virtual flow meter calibration](https://mlsanity.com/paper/2304.06310/) (2023)
- [A deep latent variable model for semi-supervised multi-unit soft sensing in industrial processes](https://mlsanity.com/paper/2407.13310/) (2024)

## Abstract (arXiv)

Steady-state process models are common in virtual flow meter applications due to low computational complexity, and low model development and maintenance cost. Nevertheless, the prediction performance of steady-state models typically degrades with time due to the inherent nonstationarity of the underlying process being modeled. Few studies have investigated how learning methods can be applied to sustain the prediction accuracy of steady-state virtual flow meters. This paper explores passive learning, where the model is frequently calibrated to new data, as a way to address nonstationarity and improve long-term performance. An advantage with passive learning is that it is compatible with models used in the industry. Two passive learning methods, periodic batch learning and online learning, are applied with varying calibration frequency to train virtual flow meters. Six different model types, ranging from data-driven to first-principles, are trained on historical production data from 10 petroleum wells. The results are two-fold: first, in the presence of frequently arriving measurements, frequent model updating sustains an excellent prediction performance over time; second, in the presence of intermittent and infrequently arriving measurements, frequent updating in addition to the utilization of expert knowledge is essential to increase the performance accuracy. The investigation may be of interest to experts developing soft-sensors for nonstationary processes, such as virtual flow meters.