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... examples/hmc.py -lattice-size 48 -beta 6.475. Currently supported options are shown in Fig. 4. This script can be used to generate gauge configurations on various lattice sizes using variable number of processes specified as a Cartesian topology. The user can change the value of β and select different integration methods, the number of time steps per MD trajectory, and the number of MD trajectories. We will add support for more ...
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... S. B. is supported by the H2020 project Numerical results were obtained using the Cyclamen cluster of The Cyprus Institute equipped with P100 GPUs. The software is implemented using the Lyncs-API [42], its interface to QUDA [43], and the QUDA library [44]. All figures were obtained by the authors under a CC BY 4.0 license, 2 unless otherwise stated. ...
We propose a unifying approach that starts from the perturbative construction of trivializing maps by Lüscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of lattice field theory and requires several orders of magnitude fewer parameters than any existing machine learning approach. Specifically, our model can achieve competitive performance with as few as 14 parameters while existing deep-learning models have around 1 million parameters for SU(3) Yang-Mills theory on a 162 lattice. This has obvious consequences for training speed and interpretability. It also provides a plausible path for scaling machine-learning approaches toward realistic theories.
We show that an infinitesimal step of gradient flow can be used for defining a novel approach for computing gradients of physical observables with respect to action parameters. Compared to the commonly used perturbative expansion, this approach does not require calculating any disconnected contribution or vacuum expectation value and can provide results up to 3 orders of magnitudes more precise. On the other hand, it requires a nontrivial condition to be satisfied by the flow action, the calculation of its force and its Laplacian, and the force of the observable, whose gradient needs to be measured. As a proof of concept, we measure gradients in β of Wilson loops in a four-dimensional SU(3) Yang-Mills theory simulated on a 164 lattice using the Wilson action.
