结合容错编码的量子化学分布式计算

doi:10.6023/A23110496

摘要/Abstract

随着大尺度模拟、机器学习等前沿应用的兴起, 分布式计算越发成为重要的计算研究手段. 然而分布式计算由于多节点导致的软硬件局限, 在科学计算、机器学习等领域的应用仍会存在一些问题. 本工作将编码分布式计算应用到量子化学领域, 通过借鉴梯度编码方案, 一方面解决分布式量子化学计算中的掉队节点问题; 另一方面增加量子化学分布式计算的自动纠错能力, 减少计算过程耗费的人力物力, 以期实现自动化的容错量子化学计算. 此外, 也提出了编码复用的计算思路, 能够简单有效地使用更多的计算资源在设定的容错能力上进行分布式计算. 最后将此计算方案应用到计算P38蛋白与配体的结合能上, 将使用编码计算得到的结果与真实的结果进行对比, 验证此方案的准确性及其在自动化容错量子化学计算方面的应用潜力.

关键词: 量子化学计算, 编码计算, 梯度编码, 容错, 自动化, 结合能

With the rise of cutting-edge applications such as large-scale simulation and machine learning, distributed computing has become more and more an important means of computational research. However, distributed computing will still have some problems in the application of scientific computing, machine learning and other fields due to the hardware and software limitations caused by multiple nodes. In this paper, we apply coded distributed computing to the field of quantum chemistry, by drawing on the gradient coding scheme, on the one hand, to solve the problem of dropped nodes in distributed quantum chemical computation; on the other hand, to increase the automatic error correction capability of quantum chemical distributed computation, to reduce the manpower and resources consumed in the computation process, with a view to realizing the automated fault-tolerant quantum chemical computation. In addition, we also propose the computational idea of coded multiplexing, which can simply and effectively use more computational resources to perform distributed computation on a set fault-tolerant capacity. We applied this computational scheme to calculate the binding energy of P38 protein and ligand by artificially specifying the use of four computational nodes for each fragment and allowing one dropout node, and compared the results obtained using coded computation with the real results, and found that the error was extremely small and negligible, and the correct results could be obtained even in the case of one dropout node or one node being miscalculated. In order to verify whether this scheme is suitable for larger scale distributed quantum chemical computation, we further randomly selected 10 fragments on the basis of coded multiplexing and performed the computation with 40 nodes at the same time, and found that the obtained results are also very accurate. Finally we calculated the binding energy of the P38 protein to the ligand, and the results obtained were consistent with previous literature, demonstrating the accuracy of this scheme and its potential for application in automated fault-tolerant quantum chemical calculations.

Key words: quantum chemical calculation, coded computing, gradient coding, fault-tolerant, automation, binding energy

引用此文

李宁, 徐丽娜, 方国勇, 马英晋. 结合容错编码的量子化学分布式计算[J]. 化学学报, 2024, 82(2): 138-145.

Ning Li, Lina Xu, Guoyong Fang, Yingjin Ma. Fault-tolerant Coded Quantum Chemical Distributed Calculation[J]. Acta Chimica Sinica, 2024, 82(2): 138-145.

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图/表 9

图1. 梯度编码的思想

Figure 1. The idea of gradient coding

算法1: 构造B矩阵
输入: n, s(s<n), 假设k=n 输出: $B ∈ R n × n$ , B矩阵的每一行有(s+1)个非零值 H=randn(s, n); H(:, n)=–sum(H(:, 1 : n–1), 2); B=zeros(n); for i=1 : n do j=mod(i–1 : s+i–1, n)+1; B(i, j)=[1; –H(:, j(2 : s+1))\H(:, j(1))]; end

算法1: 构造B矩阵
输入: n, s(s<n), 假设k=n 输出: $B ∈ R n × n$ , B矩阵的每一行有(s+1)个非零值 H=randn(s, n); H(:, n)=–sum(H(:, 1 : n–1), 2); B=zeros(n); for i=1 : n do j=mod(i–1 : s+i–1, n)+1; B(i, j)=[1; –H(:, j(2 : s+1))\H(:, j(1))]; end

算法2: 构造A矩阵
输入: 矩阵B 输出: 矩阵A for I ⊆ [n], \|I\|=(n–s) do a=zeros(1, n); x=ones(1, n)/B(I, :); a(I)=x; A=[A; a]; end

图2. MFCC框架分块示意图

Figure 2. Illustration of the MFCC framework

图3. P38蛋白(PDB ID: 3FLZ)结构图

Figure 3. The structure of P38 protein

碎片编号	参考值	梯度编码计算的能量/(a.u.)
0029	–6.94210e^-5	–6.94210e^-5
		–6.94210e^-5
		–6.94210e^-5
		–6.94210e^-5
0062	1.38461e^-4	1.38461e^-4
		(无结果)
		(无结果)
		(无结果)

表1. 梯度编码计算结果与真实结果比较

Table 1. Compare the results between these computed by gradient encoding and those from ref. 49

碎片编号	参考值	梯度编码计算的能量/(a.u.)
0130	–6.76000e^-6	–0.01000
		0.02999
		0.01999
		–6.75999e^-6
0187	1.62210e^-5	1.62210e^-5
		1.62210e^-5
		1.62210e^-5
		1.62210e^-5
0262	–2.30730e^-5	–2.30730e^-5
		–2.30730e^-5
		–2.30730e^-5
		–2.30730e^-5
0337	–1.9320e^-6	–1.9320e^-6
		–1.9320e^-6
		–1.9320e^-6
		–1.9320e^-6

表2. 梯度编码计算结果与真实结果比较

Table 2. Compare the results between these computed by gradient encoding and those from ref. 49

图4. 10个片段和配体(红色)的相关结构

Figure 4. Related structures of 10 fragments and ligand (red)

图5. 编码计算值与参考值的误差(绝对值)

Figure 5. Errors between encoded calculated values and reference values (absolute value) from ref. 49

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