# Forecasting steam mass flow in power plants using the parallel hybrid network

arXiv: https://arxiv.org/abs/2307.09483 · HTML: https://mlsanity.com/paper/2307.09483/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 69 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Recurrent Neural Networks (RNNs): A gentle Introduction and Overview](https://mlsanity.com/paper/1912.05911/) (2019)
- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Hybrid quantum neural network for drug response prediction](https://mlsanity.com/paper/2211.05777/) (2022)
- [Benchmarking simulated and physical quantum processing units using quantum and hybrid algorithms](https://mlsanity.com/paper/2211.15631/) (2022)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [Hybrid quantum ResNet for car classification and its hyperparameter optimization](https://mlsanity.com/paper/2205.04878/) (2022)
- [An exponentially-growing family of universal quantum circuits](https://mlsanity.com/paper/2212.00736/) (2022)
- [Quantum algorithms applied to satellite mission planning for Earth observation](https://mlsanity.com/paper/2302.07181/) (2023)
- [Practical application-specific advantage through hybrid quantum computing](https://mlsanity.com/paper/2205.04858/) (2022)
- [Parallel Hybrid Networks: an interplay between quantum and classical neural networks](https://mlsanity.com/paper/2303.03227/) (2023)
- [Effects of noise on the overparametrization of quantum neural networks](https://mlsanity.com/paper/2302.05059/) (2023)
- [QDNN: DNN with Quantum Neural Network Layers](https://mlsanity.com/paper/1912.12660/) (2019)
- [Bayesian Optimization For Multi-Objective Mixed-Variable Problems](https://mlsanity.com/paper/2201.12767/) (2022)
- [Day-Ahead PV Power Forecasting Based on MSTL-TFT](https://mlsanity.com/paper/2301.05911/) (2023)
- [Short-term Prediction and Filtering of Solar Power Using State-Space Gaussian Processes](https://mlsanity.com/paper/2302.00388/) (2023)
- [A generalised multi-factor deep learning electricity load forecasting model for wildfire-prone areas](https://mlsanity.com/paper/2304.10686/) (2023)

## Built on by (most cited first, 10 of 10)

- [Hybrid quantum image classification and federated learning for hepatic steatosis diagnosis](https://mlsanity.com/paper/2311.02402/) (2023)
- [A supervised hybrid quantum machine learning solution to the emergency escape routing problem](https://mlsanity.com/paper/2307.15682/) (2023)
- [Photovoltaic power forecasting using quantum machine learning](https://mlsanity.com/paper/2312.16379/) (2023)
- [Method for noise-induced regularization in quantum neural networks](https://mlsanity.com/paper/2410.19921/) (2024)
- [TQml Simulator: optimized simulation of quantum machine learning](https://mlsanity.com/paper/2506.04891/) (2025)
- [Predictive control of blast furnace temperature in steelmaking with hybrid depth-infused quantum neural networks](https://mlsanity.com/paper/2504.12389/) (2025)
- [Superposed parameterised quantum circuits](https://mlsanity.com/paper/2506.08749/) (2025)
- [Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines](https://mlsanity.com/paper/2504.20823/) (2025)
- [Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials](https://mlsanity.com/paper/2602.16908/) (2026)
- [Soft-Quantum Algorithms](https://mlsanity.com/paper/2604.06523/) (2026)

## Abstract (arXiv)

Efficient and sustainable power generation is a crucial concern in the energy sector. In particular, thermal power plants grapple with accurately predicting steam mass flow, which is crucial for operational efficiency and cost reduction. In this study, we use a parallel hybrid neural network architecture that combines a parametrized quantum circuit and a conventional feed-forward neural network specifically designed for time-series prediction in industrial settings to enhance predictions of steam mass flow 15 minutes into the future. Our results show that the parallel hybrid model outperforms standalone classical and quantum models, achieving more than 5.7 and 4.9 times lower mean squared error loss on the test set after training compared to pure classical and pure quantum networks, respectively. Furthermore, the hybrid model demonstrates smaller relative errors between the ground truth and the model predictions on the test set, up to 2 times better than the pure classical model. These findings contribute to the broader scientific understanding of how integrating quantum and classical machine learning techniques can be applied to real-world challenges faced by the energy sector, ultimately leading to optimized power plant operations. To our knowledge, this study constitutes the first parallel hybrid quantum-classical architecture deployed on a real-world power-plant dataset, illustrating how near-term quantum resources can already augment classical analytics in the energy sector.