Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due empirical constraints or high computational cost of accessing the function. In high-energy physics, precise computation scattering cross-section a process requires evaluation computationally intensive integrals. A wide variety methods machine learning have been used tackle this problem, but often motivation using one method over another lacking. Comparing these typically highly dependent on problem at hand, so we specify case where can evaluate function large number times, after which quick and accurate take place. We consider four interpolation three techniques compare their performance toy functions, four-point scalar Passarino-Veltman D_0 D0 function, two-loop self-energy master integral M. find that low dimensions (d = 3), traditional like Radial Basis Function perform very well, higher (d=5, 6, 9) multi-layer perceptrons (a.k.a neural networks) do not suffer as much from curse dimensionality provide fastest most predictions.