Leveraging neural control variates for enhanced precision in lattice field theory
This work addresses a key bottleneck in lattice QCD for physicists, enabling more precise calculations of nuclear forces, though it is incremental as it builds on existing control variate methods.
The paper tackled the problem of high uncertainty in stochastic methods for lattice field theory, particularly for observables like baryons, by using a neural network to parametrize control variates, resulting in substantial improvements, especially in the strong coupling regime.
Results obtained with stochastic methods have an inherent uncertainty due to the finite number of samples that can be achieved in practice. In lattice QCD this problem is particularly salient in some observables like, for instance, observables involving one or more baryons and it is the main problem preventing the calculation of nuclear forces from first principles. The method of control variables has been used extensively in statistics and it amounts to computing the expectation value of the difference between the observable of interest and another observable whose average is known to be zero but is correlated with the observable of interest. Recently, control variates methods emerged as a promising solution in the context of lattice field theories. In our current study, instead of relying on an educated guess to determine the control variate, we utilize a neural network to parametrize this function. Using 1+1 dimensional scalar field theory as a testbed, we demonstrate that this neural network approach yields substantial improvements. Notably, our findings indicate that the neural network ansatz is particularly effective in the strong coupling regime.