12th International Symposium on Symbiotic Nuclear Power ( ISSNP-2026)

PUREX process simulation relies on coupled empirical correlations and physicochemical equations, but large-scale calculations, parameter screening, and dynamic simulations require repeated numerical iterations and incur high computational costs[1-4]. Machine-learning surrogate models of key process parameters therefore offer a promising route to efficiency gains [4-6], with rapid, accurate prediction of distribution ratios being a central requirement. However, radiochemical solvent-extraction datasets are typically small, conditionally discrete, and expensive to acquire, limiting surrogate-model training and generalization [7–8]. To address this, we developed a conditional variational autoencoder (C-VAE) data-augmentation framework for small-sample distribution-ratio datasets of key radionuclides (U, Pu) in TBP-HNO₃ systems. Rather than learning the joint distribution of inputs and targets, the C-VAE learns the conditional distribution P(Y|X), thereby better preserving the process-variable-to-distribution-ratio mapping. On the augmented data, artificial neural network (ANN) models were trained as data-driven distribution-ratio predictors for PUREX simulation; Gaussian, CTGAN, and Copula GAN served as benchmarks under matched data size, partitioning, and evaluation conditions. Generated datasets were first assessed for statistical consistency and structural preservation using KDE, PCA, t-SNE, feature-correlation analysis, and nearest-neighbor distance; downstream ANN models were then tested on synthetic, original-training, and independent original-test sets. C-VAE data best preserved both the original statistics and inter-variable mappings, and ANNs trained on it consistently outperformed the benchmarks on real experimental data. On the three independent original test sets, these models reached R²=0.804, 0.981, and 0.953, exceeding the original-data baselines (0.610, 0.935, 0.750). As the synthetic-data fraction rose from 10% to 100%, prediction error generally decreased; for C-VAE, MAPE fell below 10% in all three systems, reaching about 4%—well below the original baseline—with improvement plateauing beyond about 60% synthetic data. This work provides a small-sample conditional data-generation and quality-evaluation framework that supports the construction of distribution-ratio surrogate models under limited radiochemical data and offers a basis for integrating fast data-driven prediction modules into PUREX process simulation.

PUREX process simulation;conditional variational autoencoder;data-driven surrogate modeling;small-sample learning;nuclear fuel reprocessing