可解释且物理信息引导的机器学习模型用于线性物质功率谱
Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning
AI总结：
本文提出了一种结合物理信息和遗传算法的可解释模拟器，用于高精度预测线性物质功率谱，适用于ΛCDM和修改引力模型。
摘要：
我们提出了一种可解释的模拟器，用于标准宇宙学模型ΛCDM中的线性物质功率谱（MPS），该模拟器通过一种结合领域知识和遗传算法的物理信息符号回归框架构建。通过将领域知识与一种名为遗传算法的机器学习技术相结合，我们探索解析表达式的空间，以推导出闭合形式、平滑、具有物理动机的MPS近似值，其精度与标准宽带重建方法如Savitzky-Golay滤波器相当。在此基础上，我们引入了透明的振荡修正，这些修正由宇宙大尺度结构中的光子声学振荡（BAO）的物理特性所指导。所得到的表达式在广泛的尺度范围内（k∈[10⁻⁵,1.5]hMpc⁻¹）提供了平均子百分比的误差，当与玻尔兹曼求解器计算的光谱进行比较时，平均偏差约为0.4%。此外，当GA衍生的公式用作非线性模拟器halofit的输入时，在较小的尺度上也保持了可比的分数偏差水平。为了展示该框架在ΛCDM之外的通用性，我们将其应用于一个代表性的f(R)引力模型。而不是训练一个通用的修改引力模拟器，我们使用玻尔兹曼求解器计算相应的线性光谱，并拟合一个参数化的变形，以修正ΛCDM平滑成分。该过程实现了平均误差在1.5-1.8%的水平，并捕捉了由修改引力引起的MPS的主要调制，使我们能够对引力对BAO尺度的影响进行受控研究。我们的结果为标准和MG宇宙学中的线性MPS提供了紧凑、准确且具有物理动机的拟合函数，为大规模结构分析中的参数推断和理论建模提供了快速且透明的替代方案。
英文摘要：
We present an interpretable emulator for the linear matter power spectrum (MPS) in the standard cosmological model $Λ$CDM, constructed via a physics-informed symbolic regression framework. By combining domain knowledge with a machine learning technique known as genetic algorithms, we explore the space of analytic expressions to derive closed-form, smooth, physically motivated approximations of the MPS that match the accuracy of standard broadband reconstruction methodologies such as the Savitzky-Golay filter. Building upon this baseline, we incorporate transparent oscillatory corrections informed by the physics of baryon acoustic oscillations (BAO). The resulting expression delivers mean sub-percent fractional errors across a broad range of scales ($k \in [10^{-5}, 1.5]~h\,\mathrm{Mpc}^{-1}$) with an average deviation of $\sim 0.4\%$ when tested against spectra computed with a Boltzmann solver. Moreover, a comparable level of fractional deviation is maintained on smaller scales when the GA-derived formulation is used as input to the nonlinear emulator halofit. To illustrate the versatility of the framework beyond $Λ$CDM, we apply it to a representative $f(R)$ gravity model. Rather than training a general modified-gravity emulator, we compute the corresponding linear spectra with a Boltzmann solver and fit a parametric deformation of the $Λ$CDM smoothed component. This procedure achieves average errors at the 1.5-1.8\% level and captures the leading modulation of the MPS induced by modified gravity, enabling a controlled study of its impact on the BAO scale. Our results provide compact, accurate, and physically motivated fitting functions for the linear MPS in both standard and MG cosmologies, offering a fast and transparent alternative to existing emulators for parameter inference and theoretical modeling in large-scale structure analyses.
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