Stochastic automatic differentiation for Monte Carlo processes

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2024-10-15 DOI:10.1016/j.cpc.2024.109396

引用次数: 0

Abstract

Monte Carlo methods represent a cornerstone of computer science. They allow sampling high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte Carlo processes, addressing the problem of obtaining derivatives (and in general, the Taylor series) of expectation values. Borrowing ideas from the lattice field theory community, we examine two approaches. One is based on reweighting while the other represents an extension of the Hamiltonian approach typically used by the Hybrid Monte Carlo (HMC) and similar algorithms. We show that the Hamiltonian approach can be understood as a change of variables of the reweighting approach, resulting in much reduced variances of the coefficients of the Taylor series. This work opens the door to finding other variance reduction techniques for derivatives of expectation values.

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蒙特卡罗过程的随机自动微分

蒙特卡罗方法是计算机科学的基石。它们允许以高效的方式对高维分布函数进行采样。在本文中，我们考虑将自动微分（Automatic Differentiation，AD）技术扩展到蒙特卡洛过程，解决获取期望值导数（以及一般情况下的泰勒级数）的问题。我们借鉴格子场理论界的观点，研究了两种方法。一种是基于重新加权，另一种是对混合蒙特卡罗（HMC）和类似算法通常使用的汉密尔顿方法的扩展。我们表明，哈密顿方法可以理解为重新加权方法的变量变化，从而大大降低了泰勒级数系数的方差。这项工作为寻找其他降低期望值导数方差的技术打开了大门。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.