This paper considers the problem of sampling from non-logconcave
distribution, based on queries of its unnormalized density. It first describes
a framework, Diffusion Monte Carlo (DMC), based on the simulation of a
denoising diffusion process with its score function approximated by a generic
Monte Carlo estimator. DMC is an oracle-based meta-algorithm, where its oracle
is the assumed access to samples that generate a Monte Carlo score estimator.
Then we provide an implementation of this oracle, based on rejection sampling,
and this turns DMC into a true algorithm, termed Zeroth-Order Diffusion Monte
Carlo (ZOD-MC). We provide convergence analyses by first constructing a general
framework, i.e. a performance guarantee for DMC, without assuming the target
distribution to be log-concave or satisfying any isoperimetric inequality. Then
we prove that ZOD-MC admits an inverse polynomial dependence on the desired
sampling accuracy, albeit still suffering from the curse of dimensionality.
Consequently, for low dimensional distributions, ZOD-MC is a very efficient
sampler, with performance exceeding latest samplers, including
also-denoising-diffusion-based RDMC and RS-DMC. Last, we experimentally
demonstrate the insensitivity of ZOD-MC to increasingly higher barriers between
modes or discontinuity in non-convex potential.

非对数凹分布下的采样问题中，提出了一种基于非归一化密度查询的采样方法，通过模拟去噪扩散过程以及用通用蒙特卡罗估计器逼近其评分函数，构建了 Diffusion Monte Carlo (DMC) 框架。进一步，通过拒绝采样实现 DMC 的 oracle，形成真正的算法 Zeroth-Order Diffusion Monte Carlo (ZOD-MC)。在不假设目标分布为对数凹或满足任何等面积不等式的情况下，提供了 DMC 的收敛性分析。证明了 ZOD-MC 具有与所需采样精度的反多项式依赖关系，但仍然受到维度诅咒的影响。因此，在低维度分布中，ZOD-MC 是一种高效的采样器，其性能超越了最新的采样器，包括基于去噪扩散的 RDMC 和 RS-DMC。最后，实验证明 ZOD-MC 对于模态之间的高屏障或非凸势能的不连续性具有不敏感性。

非对数凹分布的零阶采样方法：通过去噪扩散缓解亚稳定性

Zeroth-Order Sampling Methods for Non-Log-Concave Distributions:  Alleviating Metastability by Denoising Diffusion

We present two machine learning methodologies that are capable of predicting
diffusion Monte Carlo (DMC) energies with small datasets (~60 DMC calculations
in total). The first uses voxel deep neural networks (VDNNs) to predict DMC
energy densities using Kohn-Sham density functional theory (DFT) electron
densities as input. The second uses kernel ridge regression (KRR) to predict
atomic contributions to the DMC total energy using atomic environment vectors
as input (we used atom centred symmetry functions, atomic environment vectors
from the ANI models, and smooth overlap of atomic positions). We first compare
the methodologies on pristine graphene lattices, where we find the KRR
methodology performs best in comparison to gradient boosted decision trees,
random forest, gaussian process regression, and multilayer perceptrons. In
addition, KRR outperforms VDNNs by an order of magnitude. Afterwards, we study
the generalizability of KRR to predict the energy barrier associated with a
Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to
predict total energies of liquid water. In all cases, we find that the KRR
models are more accurate than Kohn-Sham DFT and all mean absolute errors are
less than chemical accuracy.

本文介绍了两种机器学习方法，可以预测扩散蒙特卡罗（DMC）能量，应用于纯净的石墨烯晶格、石墙缺陷、液态水等方面，KRR 模型的预测精度在比较各种模型中表现得最佳。

机器学习扩散蒙特卡罗能量

Machine Learning Diffusion Monte Carlo Energies

Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed
significant developments in the past decades and become one of the go-to
methods when accurate ground state energy of molecules and materials is needed.
The remaining bottleneck is the limitations of the inaccurate nodal structure,
prohibiting more challenging electron correlation problems to be tackled with
DMC. In this work, we apply the neural-network based trial wavefunction in
fixed-node DMC, which allows accurate calculation of a broad range of atomic
and molecular systems of different electronic characteristics. Our method is
superior in both accuracy and efficiency compared to state-of-the-art neural
network methods using variational Monte Carlo. Overall, this computational
framework provides a new benchmark for accurate solution of correlated
electronic wavefunction and also shed light on the chemical understanding of
molecules.

本文介绍了一种基于神经网络试波函数的固定节点扩散蒙特卡罗方法，支持准确计算具有不同电子特性的原子和分子系统的广泛范围，进一步提高精度和效率，并为相关化学问题提供了新的解决方案。

通过基于神经网络的扩散蒙特卡罗方法接近分子的基态

Towards the ground state of molecules via diffusion Monte Carlo on  neural networks

Recently developed neural network-based \emph{ab-initio} solutions (Pfau et.
al arxiv:1909.02487v2) for finding ground states of fermionic systems can
generate state-of-the-art results on a broad class of systems. In this work, we
improve the results for this Ansatz with Diffusion Monte Carlo. Additionally,
we introduce several modifications to the network (Fermi Net) and optimization
method (Kronecker Factored Approximate Curvature) that reduce the number of
required resources while maintaining or improving the modelling performance. In
terms of the model, we remove redundant computations and alter the way data is
handled in the permutation equivariant function. The Diffusion Monte Carlo
results exceed or match state-of-the-art performance for all systems
investigated: atomic systems Be-Ne, and the carbon cation C$^+$.

本文介绍了一种基于神经网络的 fermionic 系统的地面状态模型，使用 Diffusion Monte Carlo 改进了模型的结果，并针对模型进行了多个修改，使其在占用更少资源的同时保持或提高建模性能。 Diffusion Monte Carlo 的结果超过或与所有研究的系统的最先进性能相匹配。