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Enhancing Nuclear Reactor Core Simulation through Data-Based Surrogate Models

Perceval Beja-Battais, Alain Grossetête, Nicolas Vayatis

TL;DR

This work tackles the need for fast, accurate core simulations to support load-following MPC in nuclear power plants by developing data-driven surrogate schemes for stiff ODEs. It investigates two approaches: a Physics-Informed Transformer using a PINN framework to predict the stiff neutron flux component, and an XGBoost-based surrogate for long-horizon integration of the stiff system. Results show that the PINN can achieve sub-second 24h trajectories with modest error, while the XGBoost surrogate yields physically coherent predictions and competitive computation times, highlighting both methods as viable warm-start or replacement tools for MPC in sensitive reactor control. The findings suggest that integrating such surrogates with traditional optimization pipelines can substantially speed up decision-making in nuclear energy systems without compromising safety or interpretability, paving the way for practical digital twins and advanced load-following strategies.

Abstract

In recent years, there has been an increasing need for Nuclear Power Plants (NPPs) to improve flexibility in order to match the rapid growth of renewable energies. The Operator Assistance Predictive System (OAPS) developed by Framatome addresses this problem through Model Predictive Control (MPC). In this work, we aim to improve MPC methods through data-driven simulation schemes. Thus, from a set of nonlinear stiff ordinary differential equations (ODEs), this paper introduces two surrogate models acting as alternative simulation schemes to enhance nuclear reactor core simulation. We show that both data-driven and physics-informed models can rapidly integrate complex dynamics, with a very low computational time (up to 1000x time reduction).

Enhancing Nuclear Reactor Core Simulation through Data-Based Surrogate Models

TL;DR

This work tackles the need for fast, accurate core simulations to support load-following MPC in nuclear power plants by developing data-driven surrogate schemes for stiff ODEs. It investigates two approaches: a Physics-Informed Transformer using a PINN framework to predict the stiff neutron flux component, and an XGBoost-based surrogate for long-horizon integration of the stiff system. Results show that the PINN can achieve sub-second 24h trajectories with modest error, while the XGBoost surrogate yields physically coherent predictions and competitive computation times, highlighting both methods as viable warm-start or replacement tools for MPC in sensitive reactor control. The findings suggest that integrating such surrogates with traditional optimization pipelines can substantially speed up decision-making in nuclear energy systems without compromising safety or interpretability, paving the way for practical digital twins and advanced load-following strategies.

Abstract

In recent years, there has been an increasing need for Nuclear Power Plants (NPPs) to improve flexibility in order to match the rapid growth of renewable energies. The Operator Assistance Predictive System (OAPS) developed by Framatome addresses this problem through Model Predictive Control (MPC). In this work, we aim to improve MPC methods through data-driven simulation schemes. Thus, from a set of nonlinear stiff ordinary differential equations (ODEs), this paper introduces two surrogate models acting as alternative simulation schemes to enhance nuclear reactor core simulation. We show that both data-driven and physics-informed models can rapidly integrate complex dynamics, with a very low computational time (up to 1000x time reduction).

Paper Structure

This paper contains 17 sections, 12 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Context
  3. Related Work & Motivations
  4. Background
  5. Notations
  6. Numerical Simulation of ODEs
  7. Statistical Learning theory
  8. Artificial Neural Networks
  9. Physics-Informed Neural Networks (PINNs)
  10. Transformers
  11. Sequence-to-Sequence Learning
  12. eXtreme Gradient BOOSTing (XGBoost)
  13. Experiments
  14. ODE System
  15. Experiment 1 : Predicting the neutron flux through a Physics-Informed Transformer
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Machine Learning Framework.
  • Figure 2: Relationship Between Machine Learning (ML) and Physics-Informed (PI) Problems. The green circle illustrates the subset of ML Problems that can be solved through the usage of neural networks.
  • Figure 3: Vanilla architecture of a transformer, from vaswani2017attention.
  • Figure 4: Comparison between the neutron flux integrated by the described method and a reference (IDAS) for the given power transient. Time ($x$-axis) is displayed in minutes.
  • Figure 5: Input power $\mathrm{P}_{\mathrm{turb}}(t)$ for the two examples for the XGBoost model.
  • ...and 1 more figures