Deep Learning Surrogates Evaluate Loss-of-Coolant Scenarios 10,000 Times Faster Than Code

Key Findings · At a Glance

• ▸Static neural networks predicted blowdown and reflood peak cladding temperature with mean absolute errors of about 10 K and 22 K.
• ▸Time-parameterised networks reproduced whole transients with mean errors below 27 K for cladding temperature and 0.03 for normalised core liquid level.
• ▸The static surrogates computed 100 test cases in under a tenth of a second; the authors report roughly 10,000-fold speed gains.
• ▸One-at-a-time sensitivity results matched the reference code with an average error of 10.3 K and identified the same dominant inputs.
• ▸Wilks 95/95 upper tolerance limits from the surrogate converged with the code's, at around 1,240 K (blowdown) and 1,265 K (reflood).
• ▸Errors and model uncertainty rose at the highest reflood temperatures, which were sparsely represented in the training data.

Opportunity

Deterministic safety analysis is a foundational component of safety analysis for nuclear power plants, and the best-estimate-plus-uncertainty approach exists to reduce the conservatism built into older methods. Its price is volume. Mapping how a plant responds across the plausible spread of physical parameters means running a thermal-hydraulic system code a large number of times, and every new sensitivity question sends the analyst back to the queue.

A surrogate model that could stand in for the code, answering in a fraction of a second, would change the economics of that work. The raw material already exists, because best-estimate studies typically leave behind a library of stored runs. The question is whether a network trained on such an archive can be trusted to reproduce the code's answers.

Researchers at Universidad Politécnica de Madrid tested exactly that. They took 1,020 existing TRACE simulations of a double-ended guillotine break in the cold leg of a three-loop pressurised water reactor rated at 2,900 MWt, each varying 29 uncertain inputs, and trained deep neural networks and long short-term memory (LSTM) networks to predict peak cladding temperature and core liquid level. Of the runs, 870 were used for training, 50 for validation and 100 for testing.

Why Machine-Learning Surrogates Have Not Yet Delivered

Some earlier machine-learning forecasting approaches in nuclear safety used a sliding-window technique, feeding the network previous timesteps computed by the code to predict the next one. That can extend a forecast, but it cannot replace the code, because the model still needs code output to run. It also lets the prior output dominate the prediction, masking how the physical inputs drive the result. The Madrid models take only the 29 initial inputs, plus time for the dynamic variants, so they function as genuine substitutes.

Results

Two static networks, one for the blowdown peak and one for the reflood peak, delivered the strongest accuracy. Test-set predictions fell mostly within 3% error bands for blowdown and 5% for reflood, with mean absolute errors of 9.8 K and 21.2 K and R² values of 0.88 and 0.76. Only 8 of 200 predictions missed by more than 50 K. Reflood is the harder case: its phenomenology is more complex and less tightly tied to initial conditions.

The dynamic approach, which adds time as an input and predicts all 1,108 timesteps of a transient, also worked. Across full sequences, the LSTM reached a mean error of 24.1 K and R² of 0.96 for cladding temperature; both architectures scored R² near 0.98 for core liquid level. Errors concentrated in the quench phase, where sparser timesteps give the network less to learn from, and the networks smoothed over level oscillations rather than tracking them. For peak values specifically, time-based models underperformed: reflood R² dropped to 0.52 for the dynamic DNN.

Speed is the headline. The static surrogates computed 100 test cases in 0.08 to 0.09 seconds, and the dynamic models generated 110,800 timestep values in one to six seconds. The authors describe the gain as roughly 10,000-fold.

Crucially, the surrogates reproduced the code's analytical conclusions, not just its numbers. A one-at-a-time sensitivity study matched TRACE with an average error of 10.3 K and identified the same dominant inputs, principally film boiling and forced convection heat transfer, break discharge coefficient, fuel thermal conductivity and critical heat flux. Shapley additive explanations pointed to the same variables. A Wilks 95/95 uncertainty calculation on freshly sampled inputs, computed in under a second, converged on upper limits of around 1,240 K for blowdown and 1,265 K for reflood, matching the code-based result.

The surrogates also made cheap a study the code makes expensive: mapping how pairs of inputs interact non-linearly. That analysis showed why the reflood peak, usually lower than the blowdown peak, becomes the limiting value when dominant inputs combine unfavourably.

The Practical Applications

Assessment

The authors are candid that this is exploratory work bounded by its data. The training set came from a best-estimate study not designed for machine learning, so the highest reflood temperatures, the cases that matter most for safety margins, were thinly represented, and prediction error and model uncertainty both rose there. The surrogates under-predicted a crossed-input case of extremely low heat transfer coefficients that lay outside the training data. Accuracy was measured only against TRACE, not against physical experiment, and the models cover only this break location, timing and safety-system configuration. In their own words, "The level of confidence and accuracy required for licensing-level analysis has not been reached." They recommend supplementing archival datasets with tailored runs that densely cover the highest temperatures.

For technical buyers the pragmatic reading is clear. These surrogates are a triage and exploration tool, not a replacement for code-of-record calculations. Their value lies in cheap iteration inside well-sampled regions of the input space; their risk lies in confident answers at the extremes, which is precisely where safety cases are decided. Organisations holding large archives of best-estimate runs may already own the raw material for such tools, but any deployment would need explicit domain-of-validity checks before results inform decisions.