Generative Artificial Intelligence for Air Shower Simulation

This research introduces GAIAS2, a novel approach leveraging Generative Adversarial Networks (GANs) to significantly accelerate air shower simulations. Specifically, it employs a Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP), further enhanced with Self-Attention mechanisms. This architecture is chosen for its ability to capture complex, high-dimensional data distributions, ensuring stable and efficient adversarial training to synthesize realistic secondary particle distributions, such as muons at ground level.

GAIAS2 was trained on a dataset of 2 million proton-induced air showers generated by CORSIKA v7.7410, covering a wide energy range (1 TeV to 300 PeV). Muon state vectors (energy, position, momentum) were stored. A data-driven binning scheme converted raw particle lists into fixed-size 4D tensors (16x16x16x8) for momentum components (Px, Py, Pz) and transverse distance (r), with logarithmically scaled particle counts. The WGAN-GP model was trained for 4000 epochs (approx. 74 hours on an NVIDIA A40 GPU). An ensemble strategy, combining 57 WGANs with a Wasserstein distance < 0.1 to the training data, was used to improve mode coverage and stability.

GAIAS2 successfully reproduces critical features of underlying particle distributions, including energy and spatial spectra of muons at ground level. The ensemble of 57 networks achieved a Wasserstein distance of 0.04 to the CORSIKA training data, quantitatively demonstrating high fidelity. Post-training, the model generates 30,000 showers in under a minute on a single GPU, delivering an approximate 10^4-fold speed-up compared to full CORSIKA simulations. This substantial acceleration dramatically reduces computational time and energy consumption, validating generative AI as a viable path for high-fidelity air-shower simulations.

Future developments aim to extend GAIAS2's capabilities: 1) Generalize the model to simultaneously generate multiple particle species (muons, electrons, photons, hadrons), capturing their interdependencies. 2) Expand the training dataset to include a broader range of primary energies, inclinations, and particle types to enhance model generalizability. 3) Integrate the generative model with differentiable or hybrid simulation pipelines, enabling real-time conditioning on shower parameters and adaptive sampling across the full cosmic-ray spectrum.