利用流生成模型進行晶格點場論中多極值採樣

Abstract

本文利用機器學習生成性模型建構晶格點量子場論中對於多極值分布的採樣方法。我們釐清了以更新為基礎的採樣演算法與生成流模型在面對多極值分布的問題，透過修正損失函數和訓練模型過程，我們設計了三個改進的演算法，分別為正KL訓練、絕熱訓練以及流距離正則化。我們利用自發對稱性破缺的實純量φ^4理論來驗證這三種方法的成效，以對稱化的混和蒙地卡羅演算法作為基準，檢視諸多物理量來確認模型是否完好的採樣到各極值。我們也探討在作用量顯著對稱性破壞的情況下這些機器學習方法的效果，我們發現流距離正則演算法可以在不知道作用量位移的情況下得到正確的採樣，這是一個機器學習可能超越混和蒙地卡羅的地方。

We proposed a guideline for multimodal sampling in lattice field theory based on machine-learned generative flow models. We identified the problems in update-based and flow-based algorithms in multimodal sampling. With proper manipulation of the loss function and training procedure, one can consistently train the resulting distribution into the desired modes using symmetrized forward KL training, Adiabatic training and flow-distance regularization. These algorithms are tested on the real scalar φ^4 theory in the symmetry-broken phase. Physical quantities, such as average magnetization, are computed and benchmarked by symmetrized Hybrid Monte Carlo (HMC). We also demonstrate that the regularized model is capable of finding both modes in the potentials with an unknown shift, therefore has the potential to outperform HMC.