Application of Zone Method based Physics-Informed Neural Networks in Reheating Furnaces

TL;DR

The paper tackles real-time, accurate temperature prediction in energy-intensive reheating furnaces, where obtaining large real-world datasets for DL is challenging, so surrogate data are generated via a zone-method physics model. It develops a Physics-Informed Neural Network (PINN) that injects zone-method based Energy-Balance regularizers for gas and surface zones, with a loss defined as $\mathcal{L}_{total}=\mathcal{L}_{sup}+\lambda_{ebv}\mathcal{L}_{ebv}+\lambda_{ebs}\mathcal{L}_{ebs}$. The method is evaluated on 50 furnace configurations using IID and autoregressive settings, comparing against naive baselines, a plain MLP, and classical ML baselines, showing improved accuracy and generalization. Results indicate the PINN with EBV+EBS achieves lower RMSE/MAE and higher $R^2$ for target temperatures, especially when previous temperatures are included, demonstrating enhanced OOD generalization via physics priors. The work suggests real-world energy savings via faster, physics-guided temperature predictions and outlines future work in transfer learning for new geometries and time-series extensions such as RNNs.

Abstract

Foundation Industries (FIs) constitute glass, metals, cement, ceramics, bulk chemicals, paper, steel, etc. and provide crucial, foundational materials for a diverse set of economically relevant industries: automobiles, machinery, construction, household appliances, chemicals, etc. Reheating furnaces within the manufacturing chain of FIs are energy-intensive. Accurate and real-time prediction of underlying temperatures in reheating furnaces has the potential to reduce the overall heating time, thereby controlling the energy consumption for achieving the Net-Zero goals in FIs. In this paper, we cast this prediction as a regression task and explore neural networks due to their inherent capability of being effective and efficient, given adequate data. However, due to the infeasibility of achieving good-quality real data in scenarios like reheating furnaces, classical Hottel's zone method based computational model has been used to generate data for model training. To further enhance the Out-Of-Distribution generalization capability of the trained model, we propose a Physics-Informed Neural Network (PINN) by incorporating prior physical knowledge using a set of novel Energy-Balance regularizers.

Figures (2)

• Figure 1: This figure is best viewed in color. Sub-figure (a) Illustration of a real-world furnace, and its subdivision as different zones. Image courtesy: hu2019modelling. A darker shade of red indicates a higher temperature. Under normal conditions, temperature increases towards the discharge end. Sub-figure (b) Illustration of incorporating zone method based regularization to train a Physics-Informed Neural Network (PINN).
• Figure 2: Convergence behaviour of our method, considering: a) Supervised, b) EBV, and c) EBS terms.