变分Monte Carlo中优化大参数集的分块线性方法
A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo
摘要：
我们提出了一个修改变分蒙特卡罗的线性方法优化方案，解决了一个关键的内存瓶颈，同时保持与传统的基态变分原理和我们最近推出的变分原理的激发态的兼容性。对于具有数万个变量的波函数ansatzes，我们的修改将每个并行进程所需的存储器从数十GB减少到数百MB，使得该方法更适合于现代超级计算机体系结构，其中数据通信和每个进程的存储器消耗是主要问题。我们验证了新的优化方案在小分子测试中的功效，包括希尔伯特空间Jastrow反对称孪幂分析和实空间多Slater Jastrow展开。满意其性能，我们已经添加了优化的QMCPACK软件包，我们证明了氢环上的原型方法，使系统收敛，非微扰预测莫特绝缘体的光学带隙。
英文摘要：
We present a modification to variational Monte Carlo's linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our recently-introduced variational principle for excited states. For wave function ansatzes with tens of thousands of variables, our modification reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes, making the methodology a much better fit for modern supercomputer architectures in which data communication and per-process memory consumption are primary concerns. We verify the efficacy of the new optimization scheme in small molecule tests involving both the Hilbert space Jastrow antisymmetric geminal power ansatz and real space multi-Slater Jastrow expansions. Satisfied with its performance, we have added the optimizer to the QMCPACK software package, with which we demonstrate on a hydrogen ring a prototype approach for making systematically convergent, non-perturbative predictions of Mott-insulators' optical band gaps.
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