Title: Unexplored Opportunities for Automatic Differentiation in Astrophysics Show Chinese title

Title: 天体物理学中自动微分的未探索机会

Abstract: We present a systematic analysis of automatic differentiation (AD) applications in astrophysics, identifying domains where gradient-based optimization could provide significant computational advantages. Building on our previous work with GRAF (Gradient-based Radar Ambiguity Functions), which discovered optimal radar waveforms achieving 4x computational speedup by exploring the trade-off space between conflicting objectives, we extend this discovery-oriented approach to astrophysical parameter spaces. While AD has been successfully implemented in several areas including gravitational wave parameter estimation and exoplanet atmospheric retrieval, we identify nine astrophysical domains where, to our knowledge, gradient-based exploration methods remain unexplored despite favorable mathematical structure. These opportunities range from discovering novel solutions to the Einstein field equations in exotic spacetime configurations to systematically exploring parameter spaces in stellar astrophysics and planetary dynamics. We present the mathematical foundations for implementing AD in each domain and propose GRASP (Gradient-based Reconstruction of Astrophysical Systems & Phenomena), a unified framework for differentiable astrophysical computations that transforms traditional optimization problems into systematic exploration of solution spaces. To our knowledge, this is the first work to systematically delineate unexplored domains in astrophysics suitable for automatic differentiation and to provide a unified, mathematically grounded framework (GRASP) to guide their implementation. Show Chinese abstract

Abstract: 我们对天体物理学中自动微分（AD）应用进行了系统分析，确定了基于梯度的优化可能提供显著计算优势的领域。 在我们之前关于GRAF（基于梯度的雷达模糊函数）的工作基础上，该工作通过探索冲突目标之间的权衡空间，发现了实现4倍计算速度提升的最优雷达波形，我们将这种发现导向的方法扩展到天体物理参数空间。 虽然AD已在包括引力波参数估计和系外行星大气检索在内的几个领域成功实施，但据我们所知，在九个天体物理领域中，尽管数学结构有利，基于梯度的探索方法仍未被探索。 这些机会包括在奇异时空配置中发现爱因斯坦场方程的新解，以及在恒星天体物理学和行星动力学中系统地探索参数空间。 我们提出了在每个领域中实现AD的数学基础，并提出了GRASP（基于梯度的天体物理系统与现象重建），这是一个用于可微分天体物理计算的统一框架，将传统的优化问题转化为解决方案空间的系统探索。 据我们所知，这是第一项系统地界定适合自动微分的未探索天体物理领域的研究，并提供了一个统一的、数学上有根据的框架（GRASP）来指导其实施。