论文标题
神经网络预处理，用于求解晶格理论中的狄拉克方程
Neural-network preconditioners for solving the Dirac equation in lattice gauge theory
论文作者
论文摘要
这项工作开发了基于神经网络的预处理，以加速晶格量子场理论中Wilson-Dirac正常方程的解决方案。该方法是针对临界点附近的两种晶格schwinger模型实现的。在该系统中，发现神经网络预处理可以加速与未经验证的系统的溶液或通过基于偶数偶数或不完整的Cholesky分解的常规方法相比，偶联梯度求解器的收敛性，按照迭代和/或复杂操作的减少来衡量。还表明，对具有小晶格量的合奏进行了训练的预处理，可用于构建较大晶格量的合奏的预处理，并且性能最小。这种体积转移技术摊销了训练成本，并为将这种预调节器扩展到具有较大晶格量和四个维度的晶格场理论计算的途径。
This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical point. In this system, neural-network preconditioners are found to accelerate the convergence of the conjugate gradient solver compared with the solution of unpreconditioned systems or those preconditioned with conventional approaches based on even-odd or incomplete Cholesky decompositions, as measured by reductions in the number of iterations and/or complex operations required for convergence. It is also shown that a preconditioner trained on ensembles with small lattice volumes can be used to construct preconditioners for ensembles with many times larger lattice volumes, with minimal degradation of performance. This volume-transferring technique amortizes the training cost and presents a pathway towards scaling such preconditioners to lattice field theory calculations with larger lattice volumes and in four dimensions.
