ML4FCC

Motivation

‍Particle tracking simulations enable the identification of three regions in CERN’s accelerators. Particles that reach the highest possibly observable number of turns in the accelerator contribute to defining the stable region, whereas those that are lost at the early stages of the experiment form the unstable region. Between these stable and unstable regions exists a chaotic state, where particles make a significant number of turns but fewer than the maximum achievable. Different sets of control parameter values of the accelerator lead to different unique machine configurations, and Figure 1 illustrates three examples in which the DA is the stable region. The chaotic region depends upon the subjective threshold at which the number of turns is deemed significant and distinct from the one that formed the unstable region, leading thus to a highly noisy class that is difficult to predict.

The dataset we analyzed is big, the chaotic region is highly noisy, and parametric representations of the DA are difficult to define, raising thus two challenging objectives: i) to develop a fully automated and computationally efficient machine learning model of the stable region as a function of the accelerator control parameters; and ii) to accurately quantify uncertainty of the predictions to improve the search for optimal machine configurations that lead to the largest DA.

Proposed Approach / Solution

‍We developed a big, flexible, distributed and Heteroscedastic Spectral-Normalized Neural Process which integrates uncertainty representation in its architecture to predict the stable and (chaotic, unstable) regions now merged into the label “unstable”. We used an empirical Bayes approach to automatically and simultaneously tune all the hyperparameters during the training phase. Figure 2 shows good performance of the best model on the training, the validation and the testing sets.

Figure 3 illustrates good accuracy for three test configurations and plausible uncertainty based on the predictive variance. As expected, the uncertainty is high when the predictions are wrong, here at the boundary between the stable and unstable regions, and the uncertainty is low when the predictions look correct.

Impact

‍The results obtained in the project have the potential to revolutionize accelerator design by focusing the automated tracking of particles only on stable areas of the phase space since particles in the unstable areas will anyway be lost. This will optimize the performance of an expensive research infrastructure, and will enable faster scientific discoveries.