A machine learning approach for efficient multi-dimensional integration
This work addresses the challenge of efficient multi-dimensional integration, which is crucial for fields like physics and finance, by offering a novel method that significantly improves accuracy over existing algorithms.
The paper tackles the problem of multi-dimensional integration by proposing a machine learning algorithm that uses regression to approximate integrands and corrects bias for unbiased estimates with statistically correct error estimation. The results show that for the same number of integrand evaluations, the new algorithm reduces uncertainties by more than an order of magnitude compared to the VEGAS algorithm in most test cases.
We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral. Then, the difference between the approximation and the true answer is calculated to correct the bias in the approximation of the integral induced by a ML prediction error. Because of the bias correction, the final estimate of the integral is unbiased and has a statistically correct error estimation. The performance of the proposed algorithm is demonstrated on six different types of integrands at various dimensions and integrand difficulties. The results show that, for the same total number of integrand evaluations, the new algorithm provides integral estimates with more than an order of magnitude smaller uncertainties than those of the VEGAS algorithm in most of the test cases.