发表机构
SISSA; INFN Sezione di Trieste; IFPU - Institute for Fundamental Physics of the Universe（国际高等研究学院; 的里雅斯特国家核物理研究所; 宇宙基础物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出SINFONIA系列三种保结构神经流架构，将其应用于2.5PN中子星旋进，实现了高精度长时轨道积分，可用于引力波建模与物理推断，性能优于基准积分器。
AI 中文摘要
长时引力波建模需同时解析快速轨道运动与慢耗散演化，同时防止小数值误差累积为长期相位漂移。本文探究能否将有限时间演化图本身作为显式、可微且保结构的对象进行学习，再通过完整旋进过程重复组合。我们构建了三种神经流架构：基于Galley双倍相空间的辛与类辛流[SINFONIA-J0]；泰勒锚定流[SINFONIA-J1]；以及在相互作用表象中学习有限时间耗散修正的马格努斯流[SINFONIA-J2]。将其应用于2.5PN中子星旋进时，三者均揭示出相同的控制机制：长期精度不仅取决于逐点映射误差，还取决于其在能量-角动量平衡所固定的单个长期通道上的符号投影。编码该结构可使学习到的映射在10²至10⁵个窗口组合（对应至并合，时间步长为完整轨道周期及以上）中保持精度，链状相位误差比基准类辛积分器低数个数量级且成本更低。该长期结构还可用于物理推断：当通道未受约束时，累积相位保留足够信息以恢复未建模的类动力摩擦力，既可以参数形式也可作为与分离度相关的学习函数。网络关闭控制可分离学习对每个映射内置解析结构的贡献。这些结果为保结构学习演化图作为引力波源建模中快速长时积分与物理推断工具的概念提供了验证。
英文摘要
Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.
Comments21 pages, 1 table, 5 figures. Comments welcomed
