论文标题
培训和投影：多体物理的减少基础方法模拟器
Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics
论文作者
论文摘要
我们介绍了减少的基础方法，作为在核多体问题的背景下开发具有可调参数的方程式的模拟器的工具。该方法使用一组解决方案为模型参数值提供的基础扩展，然后在精心挑选的低维子空间上投射方程。我们将特征向量延续文献中的一些结果与减少基础方法的形式主义联系起来，并显示如何将这些方法应用于广泛的问题。正如我们所说明的，正式主义对此类问题的可能成功可以通过主要成分分析事先诊断。我们将简化的基本方法应用于具有谐波捕获势的一维总壁杆菌方程，并将其用于$^{48} $ CA的核密度功能理论，与传统求解器相比，在这两种情况下，在这两种情况下均达到了X150的速度超过X150。该方法的出色性能以及其直接实施的实施，显示出其在仿真计算要求计算（包括不确定性量化）中的应用的希望。
We present the reduced basis method as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connect some of the results in the eigenvector continuation literature to the formalism of reduced basis methods and show how these methods can be applied to a broad set of problems. As we illustrate, the possible success of the formalism on such problems can be diagnosed beforehand by a principal component analysis. We apply the reduced basis method to the one-dimensional Gross-Pitaevskii equation with a harmonic trapping potential and to nuclear density functional theory for $^{48}$Ca, achieving speed-ups of more than x150 in both cases when compared to traditional solvers. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.
