Open Access

ARTICLE

Data-Driven and Physics-Informed Surrogate Modeling for Heat Conduction in the Pressurizer Wall of Pressurized Water Reactors under Severe Accident Scenarios

Fabiano Thulu, Zeyun Wu^*

Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA, USA

* Corresponding Author: Zeyun Wu. Email:

(This article belongs to the Special Issue: Neutronic and Thermal-Hydraulic Analysis of Advanced Nuclear Reactors)

Energy Engineering 2026, 123(5), 1 https://doi.org/10.32604/ee.2026.076328

Received 18 November 2025; Accepted 22 January 2026; Issue published 27 April 2026

Abstract

Real-time prediction of temperature distribution in the pressurizer walls of Pressurized Water Reactors (PWRs) during severe accidents, such as Station Blackout (SBO) and Loss-of-Coolant Accident (LOCA) is vital for structural integrity assessment. However, conventional thermal-hydraulic simulations used for such predictions are computationally intensive, limiting their applicability for real-time analysis. This study develops and compares three surrogate models: Polynomial Regression, Deep Neural Network (DNN), and a Physics-Informed Neural Network (PINN). Thermal-hydraulic simulation data generated by RELAP5-3D are integrated with physics-constrained learning techniques to model transient heat conduction in the pressurizer wall. The internal wall temperature evolution is reconstructed using a one-dimensional transient heat conduction mode solved via the Finite Difference Method. The Polynomial Regression model, while achieving a relative high coefficient of determination (R2=0.9780), exhibited an average Root Mean Squared Error (RMSE) of 7.50 K and a Maximum Absolute Error (MaxAE) of 193.6 K on unseen test data, indicating limited capability in capturing localized thermal stresses. In contrast, the purely data-drive DNN model demonstrated superior performance, achieving an overall test R2 of 0.9996, an RMSE of 1.04 K, and a significantly reduced MaxAE of 24.8 K. Finally, the PINN model yielded an overall physics-based test R2 of 0.9874, with an RMSE of 5.66 K, and a MaxAE of 89.7 K. Although the DNN achieves the highest statistical accuracy, the PINN offers a key advantage by enforcing adherence to the governing heat conduction equations. The embedded physical consistency makes PINN a more reliable and trustworthy surrogate for nuclear safety analysis, where maintaining physical fidelity is as critical as numerical accuracy.

---

Keywords

---