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DOE OSTI2025

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

ML-based Micro-CT SOFC Microstructure Models (from Kent 2026 Microstructural Augmentation paper)

Overview -------------------------- This repository contains datasets from the manuscript **"Enhanced Generalizability to Deep-Learning Quantification of 3D Microstructural Characteristics through Microstructurally Aware Augmentation of Scarce Data"** (*William F. Kent, Rochan Bajpai, Rachel C. Kurchin, William K. Epting, Harry W. Abernathy, Paul A. Salvador. Submitted 2026*). The methods are also described in the dissertation **Data Intensive Analysis of Solid Oxide Cell Microstructures** (*Doctoral dissertation, Carnegie Mellon University, 2025*). The datasets here are trained convolutional neural network (CNN) models for predicting key microstructural properties of solid oxide cell (SOC) electrodes from low-res, 2-channel 3D images, as well as some helpful code. The parameters for input images are provided in the paper. Sample data is provided in the file `Combined_anode_aug_dual_1k_examples` - that particular data was used to train `anode_all_aug.pth` and will work most accurately with that model. Please familiarize yourself with all caveats on accuracy and applicability, as detailed in the associated paper. Usage -------------------------- The basic usage is as follows, assuming `model_fn` is the path to the .pth file, and `X` is 2-channel input image(s) of the proper dimensions (either one image of shape `[2,12,24,24]`, or a batch of N input images of shape `[N,2,12,24,24]`): from CNN_inferencer import load_model_for_inference model = load_model_for_inference(model_fn) y_predicted = model(X) The model object automatically handles input scaling and output de-scaling based on the way the models were trained - in other words, pass in a 2-channel micro-CT image, and it will output microstructural property values in real units. ## Other model object attributes Note that model has useful attributes other than its forward pass model(X). * `model.output_descaler` - returns the output descaler object. Model does the de-scaling when generating inferences, but you may want to re-use this de-scaler on other values to e.g. compare predictions to ground truth from already-scaled training data. * `model.prop_names` - Gives the property names of the predicted y values, in order. Only exists if there's an output scaler as part of the model object, which there will be in the models provided here. ## Usage with sample data Here is a short script to use with the included sample data. from CNN_inferencer import display_predictions, load_model_for_inference, calculate_mape, parity_plot import h5py import numpy as np model_fn = 'anode_all_aug.pth' data_fn = 'Combined_anode_aug_dual_1k_examples.h5' N_samples = 200 figure_outdir = '.' model = load_model_for_inference(model_fn) with h5py.File(data_fn,'r') as f: XX = f['X'] #These are the 2-channel 3D images yy = f['y'] #These are the ground-truth microstructural properties, but they have been scaled for training - need to de-scale below N = XX.shape[0] #How many images total in the input data file #Run inferences on N_samples random samples from XX. #Run in a batch, much more efficient than one at a time. ii = np.random.choice(N,N_samples,replace=False) ii.sort() y_pred = model(XX[ii]) #Get the original/true (but normalized/scaled) values from the training dataset... #Because they were normalized, they are not in real units yet. So let's also de-scale them using model.output_scaler. y_true = model.output_scaler.transform(yy[ii]) #Let's display actual values for just 5 random ones for i in np.random.choice(N_samples,5,replace=False): display_predictions(y_true[i], y_pred[i], model.prop_names) #Make parity plots for each property (ground truth vs predicted values) #Also label each plot with the mean abs. percent error (MAPE) of the predicted values for i,key in enumerate(model.prop_names): mape = calculate_mape(y_true[:,i], y_pred[:,i]) parity_plot(y_true[:,i], y_pred[:,i], figure_outdir, key, extra_title=f' ({mape:.2f}% MAPE)')

3D microstructure↗
DOE OSTI2025

Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches

Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.

Advanced reactors↗