Self-learning Monte Carlo method with Behler-Parrinello neural networks
Self-learning Monte Carlo method with Behler-Parrinello neural networks
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DOI：
10.1103/physrevb.101.115111
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发表时间：
2018-07
影响因子：
3.7
通讯作者：
Y. Nagai;M. Okumura;A. Tanaka
中科院分区：
文献类型：
--
作者：
Y. Nagai;M. Okumura;A. Tanaka
我们提出了一种通用的方法来构建一个有效的哈密顿量的自学习蒙特卡罗方法（SLMC），通过训练一个有效的模型，提出不相关的配置在马尔可夫链，加快蒙特卡罗模拟。然而，它的应用是有限的。这是因为找到有效哈密顿量的显式形式并不明显。特别是，很难使可训练的有效哈密顿包括多体相互作用。为了克服这一关键困难，我们引入了Behler-Parrinello神经网络（BPNNs）作为没有任何先验知识的“有效哈密顿”，用于构建分子动力学中相互作用多粒子系统的势能面。我们将联合收割机和BPNN结合起来，通过关注哈密顿量的可分性，提出了如何构造逐元素配置。我们将其应用于量子杂质模型。我们观察到显着改善的接受比从0.01（显式形式的有效哈密顿量）到0.76（BPNN）。这意味着BPNN有效哈密顿量包含了许多体相互作用，而显式有效哈密顿量中忽略了体相互作用。BPNN使SLMC更有前途。
We propose a general way to construct an effective Hamiltonian in the Self-learning Monte Carlo method (SLMC), which speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. Its applications are, however, limited. This is because it is not obvious to find the explicit form of the effective Hamiltonians. Particularly, it is difficult to make trainable effective Hamiltonians including many-body interactions. In order to overcome this critical difficulty, we introduce the Behler-Parrinello neural networks (BPNNs) as "effective Hamiltonian'' without any prior knowledge, which is used to construct the potential-energy surfaces in interacting many particle systems for molecular dynamics. We combine SLMC with BPNN by focusing on a divisibility of Hamiltonian and propose how to construct the element-wise configurations. We apply it to quantum impurity models. We observed significant improvement of the acceptance ratio from 0.01 (the effective Hamiltonian with the explicit form) to 0.76 (BPNN). This drastic improvement implies that the BPNN effective Hamiltonian includes many body interaction, which is omitted in the effective Hamiltonian with the explicit forms. The BPNNs make SLMC more promising.