无需高分辨率标签，用物理约束实现黑洞合并模拟的超分辨率重建
Super-Resolution without High-Resolution Labels for Black Hole Simulations
- 利用广义相对论的哈密顿量与动量约束作为指导信号
- 约束违反度降低一到两个数量级，显著提升模拟精度
- 适用于分布外数据，适合缺乏标注的极端天体物理仿真
生成高分辨率模拟对于深入理解宇宙中最剧烈的事件之一——黑洞合并至关重要。然而，由于计算成本过高和可扩展性问题，当前方法受限于合理时间与资源内所能达到的模拟保真度与分辨率。本文提出一种新方法，通过超分辨率技术在无需直接使用高分辨率标签的情况下，利用广义相对论中的哈密顿量与动量约束（fundamental equations）来引导时空演化。实验表明，该方法使约束违反度降低一至两个数量级，并在分布外模拟上表现出良好泛化能力。
原文摘要 · Abstract (English)
Generating high-resolution simulations is key for advancing our understanding of one of the universe's most violent events: Black Hole mergers. However, generating Black Hole simulations is limited by prohibitive computational costs and scalability issues, reducing the simulation's fidelity and resolution achievable within reasonable time frames and resources. In this work, we introduce a novel method that circumvents these limitations by applying a super-resolution technique without directly needing high-resolution labels, leveraging the Hamiltonian and momentum constraints-fundamental equations in general relativity that govern the dynamics of spacetime. We demonstrate that our method achieves a reduction in constraint violation by one to two orders of magnitude and generalizes effectively to out-of-distribution simulations.
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