A Surrogate Model for Proton Spectrum Prediction to Map Transitions in Laser-Ion Acceleration

Researchers have developed a novel physics-guided, decoupled dual-branch surrogate model capable of predicting continuous proton energy spectra from laser-driven ion acceleration experiments. The model integrates a $\beta$-VAE for feature extraction with a multi-layer perceptron for boundary enforcement.

The framework demonstrates high predictive accuracy, achieving an $R^2$ of 0.94 for maximum cutoff energy and total particle flux. It also shows a median per-sample spectral $R^2$ of 0.985 in $\log_{10}$ space across a 2000-bin energy distribution.

The surrogate model incorporates uncertainty quantification through deep ensembles, functioning as a probabilistic diagnostic tool with calibration errors below 6.2%. It successfully reproduces spectral signatures indicative of transitions between Target Normal Sheath Acceleration (TNSA) and Relativistically Induced Transparency (RIT) and Breakout Afterburner (BOA) dynamics.