发表机构
Universidad Nacional de Colombia; University of Nottingham; Queen Mary University of London; The University of Edinburgh（哥伦比亚国立大学; 诺丁汉大学; 伦敦大学皇家玛丽学院; 爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用自动微分高效定位数值相对论中的临界解，以标量临界坍缩为例，在二维参数空间中仅用35次运行找到临界线，并验证了不稳定模式的普适性，方法可扩展至高维参数空间。
AI 中文摘要
数值相对论是一个术语，用于描述通过数值方法将完整的非线性爱因斯坦方程作为初值问题进行求解。单个模拟在计算上非常昂贵，并且在许多应用中，参数空间的高复杂性和解的非线性敏感性使得定位特定感兴趣的结果具有挑战性。在这项工作中，我们展示了自动微分如何高效地找到感兴趣的动力学解，并以标量临界坍缩这一经典问题作为原理验证。我们在二维参数空间中定位了一条临界解线，仅需35次运行，而使用二分法定位10个临界点则需要270次运行；我们还直接计算了不稳定模式，并确认了其沿该线的普适性。该方法可轻松扩展到更高维的参数空间，为在强动力学引力区域中高效定位更复杂的解提供了一种有前景的方法。
英文摘要
Numerical relativity is a term used to describe the solution of the full non-linear Einstein Equations as an initial value problem using numerical methods. Individual simulations are computationally expensive and in many applications the high complexity of the parameter space and non-linear sensitivity of the solutions makes locating particular outcomes of interest challenging. In this work, we demonstrate how auto-differentiation can efficiently find dynamical solutions of interest, using the classic problem of scalar critical collapse as a proof of principle. We locate a line of critical solutions in a 2D parameter space using 35 runs, compared to the 270 runs required to locate 10 critical points using bisection, and directly calculate the unstable mode, confirming its universality along the line. The method is straightforwardly extendable to higher-dimensional parameter spaces, offering a promising method to efficiently target more complex solutions in strong dynamical gravity regimes.
