STAR-XPC: Set Transformer for Estimating X-ray Transmission in Polymer Composites

A Set Transformer neural network predicts X-ray transmission ratios through polymer composites in 1-3 milliseconds, versus the 20,000-second (over 5 hours) limit on each Monte Carlo reference simulation, according to an arXiv paper (2610.28709v1). The model embeds each of up to 11 molecular constituents with the chemistry-pretrained ChemBERTa language model and was trained on 4,697 PENELOPE/penEasy-simulated configurations at 30, 80, 100 and 120 kV over polyethylene-based slabs 0.15-2.5 mm thick, reaching MSE of (1.12 ± 0.56)×10⁻⁴, NMSE% of 0.0294% ± 0.0147% and R² = 0.9988 under leakage-free, jointly stratified 10-fold cross-validation. Per-sample errors gave an alpha-trimmed (α = 0.10) absolute percentage error of 1.66% and a median APE of 1.15%, offering radiation-shielding researchers a fast surrogate for photon-history-capped Monte Carlo transport simulation.

arXiv:2610.28709v1 Announce Type: new Abstract: Evaluating the energy transmission ratio of an X-ray beam through a polymer composite is a challenging task in radiation shielding studies. The reference solution with Monte Carlo transport simulation is highly accurate but computationally expensive: each of our reference simulations is capped at $4\times10^9$ photon histories and a 20,000 s over 5 hours time limit, while closed-form analytical methods fail to represent such complex scenarios. We present an artificial neural network model that maps the unordered multi-set of molecular constituents, their mass fractions, and four bulk physical descriptors directly to the transmission ratio $I t /I 0$ in 1-3 milliseconds. The model is a Set Transformer, which makes it permutation invariant by construction and accepts mixtures of different sizes up to 11 constituents within a fixed-size padded set. Each constituent is embedded with a chemistry-pretrained transformer language model, ChemBERTa. In our proposed method, training data are produced by an automated PENELOPE/penEasy pipeline using the radiation source at 30, 80, 100, and 120 kV tube voltages over polyethylene-based shielding composite slabs of thicknesses spanning 0.15-2.5 mm. After preprocessing, the dataset contains $n = 4697$ simulated configurations on which a leakage-free, jointly stratified 10-fold cross-validation is performed, attaining mean squared error MSE = $ 1.12 \pm 0.56 \times10^{-4}$, normalized-MSE percentage NMSE% = 0.0294% $\pm$ 0.0147%, and $R^2 = 0.9988$. The corresponding per-sample percentage errors give an alpha-trimmed $\alpha = 0.10$ absolute percentage error APE of 1.66% and a median APE of 1.15%. Our model's inference is several orders of magnitude faster than the underlying Monte Carlo simulation sub-millisecond per query vs. several hours for the reference run with effective accuracy in predicting $I t /I 0$.