Flexible Spectral-Normalized Neural Gaussian Process for Dynamic Aperture Prediction

In large-scale scientific applications, such as particle accelerator physics, quantifying uncertainty is essential for decision-making but often computationally prohibitive. Traditional methods like Deep Ensembles are resource-intensive, while existing semi-Bayesian models like SNGP often require manual, time-consuming hyperparameter tuning. The authors aim to develop a scalable, automated, and uncertainty-aware model that can be trained efficiently without manual intervention.

The authors propose an empirical Bayes framework for a flexible, heteroscedastic version of the Spectral-normalized Neural Gaussian Process (auto-hetSNGP). The key innovation is the separation of model parameters into two distinct sets: deterministic parameters (learned during training) and stochastic parameters (used for posterior sampling at inference). By integrating hyperparameter estimation directly into the training loop and utilizing a preconditioned Newton-Raphson procedure for posterior inference, the model avoids the need for costly manual tuning. The authors validate this approach by predicting the dynamic aperture (DA) of the Large Hadron Collider (LHC) at CERN, a task that typically requires massive, time-consuming particle-tracking simulations.

The auto-hetSNGP model achieves predictive performance competitive with state-of-the-art methods like Deep Deterministic Uncertainty (DDU) while requiring significantly fewer training epochs. Crucially, the model produces well-calibrated uncertainty estimates that are more consistent and interpretable than those of DDU, particularly in challenging, configuration-specific test cases where other models often exhibit overconfidence or misrepresent class boundaries. The empirical Bayes approach successfully automates the learning of regularization levels, making the model highly practical for resource-constrained scientific environments.