# A deep latent variable model for semi-supervised multi-unit soft sensing in industrial processes

arXiv: https://arxiv.org/abs/2407.13310 · HTML: https://mlsanity.com/paper/2407.13310/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 16 of 16)

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- [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)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Towards a Neural Statistician](https://mlsanity.com/paper/1606.02185/) (2016)
- [Multi-Level Variational Autoencoder: Learning Disentangled Representations from Grouped Observations](https://mlsanity.com/paper/1705.08841/) (2017)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Multi-task learning for virtual flow metering](https://mlsanity.com/paper/2103.08713/) (2021)
- [Semi-supervised Learning for Data-driven Soft-sensing of Biological and Chemical Processes](https://mlsanity.com/paper/2107.13822/) (2021)
- [Passive learning to address nonstationarity in virtual flow metering applications](https://mlsanity.com/paper/2202.03236/) (2022)
- [Modeling Task Relationships in Multi-variate Soft Sensor with Balanced Mixture-of-Experts](https://mlsanity.com/paper/2305.16360/) (2023)
- [Multi-task and few-shot learning in virtual flow metering](https://mlsanity.com/paper/2309.15828/) (2023)

## Abstract (arXiv)

In many industrial processes, an apparent lack of data limits the development of data-driven soft sensors. There are, however, often opportunities to learn stronger models by being more data-efficient. To achieve this, one can leverage knowledge about the data from which the soft sensor is learned. Taking advantage of properties frequently possessed by industrial data, we introduce a deep latent variable model for semi-supervised multi-unit soft sensing. This hierarchical, generative model is able to jointly model different units, as well as learning from both labeled and unlabeled data. An empirical study of multi-unit soft sensing is conducted using two datasets: a synthetic dataset of single-phase fluid flow, and a large, real dataset of multi-phase flow in oil and gas wells. We show that by combining semi-supervised and multi-task learning, the proposed model achieves superior results, outperforming current leading methods for this soft sensing problem. We also show that when a model has been trained on a multi-unit dataset, it may be finetuned to previously unseen units using only a handful of data points. In this finetuning procedure, unlabeled data improve soft sensor performance; remarkably, this is true even when no labeled data are available.