Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation
Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation
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DOI：
10.1016/j.jcp.2022.111765
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发表时间：
2021-12
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影响因子：
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通讯作者：
Jeffmin Lin;Gil Goldshlager;Lin Lin-Lin
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文献类型：
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作者：
Jeffmin Lin;Gil Goldshlager;Lin Lin-Lin
神经网络和量子蒙特卡罗方法的结合已成为高精度电子结构计算的一条有前途的道路。先前的提议将等变神经网络层与最终反对称层相结合，以满足电子波函数的反对称要求。然而，迄今为止，尚不清楚是否可以表示具有物理意义的反对称函数，并且很难精确测量反对称层的表现力。这项工作试图通过引入明确的反对称通用神经网络层来解决这个问题。这种方法的计算成本随着系统大小的增加而增加，但我们仍然能够将其应用于小型系统，以更好地理解反对称层的结构如何影响其性能。我们首先介绍一个通用的反对称 (GA) 神经网络层，我们用它来替换称为 FermiNet 的高精度模拟的整个反对称层。我们证明了由此产生的 FermiNet-GA 架构可以有效地产生小原子和分子的精确基态能量。然后，我们考虑分解反对称（FA）层，它通过用反对称神经网络的乘积替换行列式的乘积来更直接地推广 FermiNet。有趣的是，我们发现最终的 FermiNet-FA 架构并没有明显优于 FermiNet。这强烈表明反对称乘积之和是 FermiNet 架构的一个关键限制方面。为了进一步探索这一点，我们研究了 FermiNet 的轻微修改，称为完整行列式模式，它将行列式的每个乘积替换为单个组合行列式。我们发现，完整的单行列式 FermiNet 弥补了标准单行列式 FermiNet 和 FermiNet-GA 在小型原子和分子问题上的很大一部分差距。令人惊讶的是，在解离键长度为 4.0 Bohr 的氮分子上，完整的单行列式 FermiNet 可以优于具有 64 个行列式的最大标准 FermiNet 计算。
The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. This work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.