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Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations
by Ibrahim Chahrour, James D. Wells
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ibrahim Chahrour |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2111.14788v3 (pdf) |
| Date accepted: | 2022-05-10 |
| Date submitted: | 2022-03-30 03:11 |
| Submitted by: | Chahrour, Ibrahim |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman $D_0$ function, and the two-loop self-energy master integral $M$. We find that in low dimensions ($d = 3$), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions ($d=5, 6, 9$) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.
List of changes
- Title changed from "Function Approximation for High-Energy Physics: Comparing Machine Learning and Interpolation Methods" to "Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations"
- Added references [7], [8], [16], [17], [18]
- Clarified the results of previous papers in the introduction, in particular the gain in speed of references [9] and [10]
- Clarified the current state of Machine Learning methods in the field of high-energy physics in the introduction
Published as SciPost Phys. 12, 187 (2022)
Reports on this Submission
Report 1 by Simon Badger on 2022-4-5 (Invited Report)
Report
I was happy to read the responses to both referee reports and am happy with the improvements that have been made to the article.
I can recommend it for publication in its current form.