Neural networks can be FLOP-efficient integrators of 1D oscillatory integrands

We demonstrate that neural networks can be FLOP-efficient integrators of one-dimensional oscillatory integrands. We train a feed-forward neural network to compute integrals of highly oscillatory 1D functions. The training set is a parametric combination of functions with varying characters and oscillatory behavior degrees. Numerical examples show that these networks are FLOP-efficient for sufficiently oscillatory integrands with an average FLOP gain of 1000 FLOPs. The network calculates oscillatory integrals better than traditional quadrature methods under the same computational budget or number of floating point operations. We find that feed-forward networks of 5 hidden layers are satisfactory for a relative accuracy of 0.001. The computational burden of inference of the neural network is relatively small, even compared to inner-product pattern quadrature rules. We postulate that our result follows from learning latent patterns in the oscillatory integrands that are otherwise opaque to traditional numerical integrators.

The Optimal use of Segmentation for Sampling Calorimeters

One of the key design choices of any sampling calorimeter is how fine to make the longitudinal and transverse segmentation. To inform this choice, we study the impact of calorimeter segmentation on energy reconstruction. To ensure that the trends are due entirely to hardware and not to a sub-optimal use of segmentation, we deploy deep neural networks to perform the reconstruction. These networks make use of all available information by representing the calorimeter as a point cloud. To demonstrate our approach, we simulate a detector similar to the forward calorimeter system intended for use in the ePIC detector, which will operate at the upcoming Electron Ion Collider. We find that for the energy estimation of isolated charged pion showers, relatively fine longitudinal segmentation is key to achieving an energy resolution that is better than 10% across the full phase space. These results provide a valuable benchmark for ongoing EIC detector optimizations and may also inform future studies involving high-granularity calorimeters in other experiments at various facilities.