Self-learning Emulators and Eigenvector Continuation
Self-learning Emulators and Eigenvector Continuation
复制标题
自学习模拟器和特征向量延拓
作者：
Avik Sarkar;Dean Lee
模拟器能够以高精度和高速度绕过计算成本高昂的科学计算，可以实现基础科学的新研究以及更多潜在的应用。在这项工作中，我们讨论使用自学习模拟器有效地求解约束方程组。自学习模拟器是一种主动学习协议，可与任何在选定训练点忠实再现精确解决方案的模拟器一起使用。关键因素是对仿真器误差的快速估计，随着仿真器的改进，误差估计的准确性会逐渐提高，并且可以使用机器学习来纠正误差估计的准确性。我们用三个例子来说明。第一个使用三次样条插值来找到具有可变系数的超越方程的解。第二个示例对样条仿真器和简化基法仿真器进行比较，以找到参数化微分方程的解。第三个示例使用特征向量连续来查找取决于多个控制参数的大型哈密顿矩阵的特征向量和特征值。
Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of constraint equations efficiently using a self-learning emulator. A self-learning emulator is an active learning protocol that can be used with any emulator that faithfully reproduces the exact solution at selected training points. The key ingredient is a fast estimate of the emulator error that becomes progressively more accurate as the emulator is improved, and the accuracy of the error estimate can be corrected using machine learning. We illustrate with three examples. The first uses cubic spline interpolation to find the solution of a transcendental equation with variable coefficients. The second example compares a spline emulator and a reduced basis method emulator to find solutions of a parameterized differential equation. The third example uses eigenvector continuation to find the eigenvectors and eigenvalues of a large Hamiltonian matrix that depends on several control parameters.
DOI：
10.1140/epja/s10050-020-00290-x
发表时间：
2021-03
期刊：
The European Physical Journal A
影响因子：
--
作者：
P. Bedaque;A. Boehnlein;M. Cromaz;M. Diefenthaler;L. Elouadrhiri;T. Horn;M. Kuchera;D. Lawrence
通讯作者：
P. Bedaque;A. Boehnlein;M. Cromaz;M. Diefenthaler;L. Elouadrhiri;T. Horn;M. Kuchera;D. Lawrence
使用特征向量连续进行散射的高效模拟器
影响因子：
4.4
作者：
Furnstahl, R.J.;Garcia, A.J.;Millican, P.J.;Zhang, Xilin
通讯作者：
Zhang, Xilin
影响因子：
4.4
作者：
Melendez, J.A.;Drischler, C.;Garcia, A.J.;Furnstahl, R.J.;Zhang, Xilin
通讯作者：
Zhang, Xilin