We present DE-VAE, a variational autoencoder (VAE) architecture to search for a compressed representation of dynamical dark energy (DE) models in observational studies of the cosmic large-scale structure. DE-VAE is trained on matter power spectra boosts generated at wavenumbers $k\in(0.01-2.5) \ h/\rm{Mpc}$ and at four redshift values $z\in(0.1,0.48,0.78,1.5)$ for the most typical dynamical DE parametrization with two extra parameters describing an evolving DE equation of state. The boosts are compressed to a lower-dimensional representation, which is concatenated with standard cold dark matter (CDM) parameters and then mapped back to reconstructed boosts; both the compression and the reconstruction components are parametrized as neural networks. Remarkably, we find that a single latent parameter is sufficient to predict 95% (99%) of DE power spectra generated over a broad range of cosmological parameters within $1\sigma$ ($2\sigma$) of a Gaussian error which includes cosmic variance, shot noise and systematic effects for a Stage IV-like survey. This single parameter shows a high mutual information with the two DE parameters, and these three variables can be linked together with an explicit equation through symbolic regression. Considering a model with two latent variables only marginally improves the accuracy of the predictions, and adding a third latent variable has no significant impact on the model's performance. We discuss how the DE-VAE architecture can be extended from a proof of concept to a general framework to be employed in the search for a common lower-dimensional parametrization of a wide range of beyond-$\Lambda$CDM models and for different cosmological datasets. Such a framework could then both inform the development of cosmological surveys by targeting optimal probes, and provide theoretical insight into the common phenomenological aspects of beyond-$\Lambda$CDM models.

翻译：我们提出了DE-VAE，一种变分自编码器（VAE）架构，用于在宇宙大尺度结构的观测研究中寻找动力学暗能量（DE）模型的压缩表示。DE-VAE在波数$k\in(0.01-2.5) \ h/\rm{Mpc}$和四个红移值$z\in(0.1,0.48,0.78,1.5)$处生成的物质功率谱增强上进行训练，这些增强基于最典型的动力学DE参数化模型，该模型用两个额外参数描述演化的DE状态方程。增强被压缩为低维表示，该表示与标准冷暗物质（CDM）参数拼接后，再映射回重建的增强；压缩和重建组件均被参数化为神经网络。值得注意的是，我们发现单个潜在参数足以预测在广泛宇宙学参数范围内生成的DE功率谱的95%（99%），其误差在包含宇宙方差、散粒噪声和类第四阶段巡天系统效应的$1\sigma$（$2\sigma$）高斯误差范围内。该单一参数与两个DE参数具有较高的互信息，并且这三个变量可以通过符号回归用显式方程联系起来。考虑具有两个潜在变量的模型仅略微提高了预测精度，而添加第三个潜在变量对模型性能没有显著影响。我们讨论了如何将DE-VAE架构从一个概念验证扩展为一个通用框架，用于在广泛的超越$\Lambda$CDM模型和不同宇宙学数据集中寻找共同的低维参数化。这样的框架既可以指导宇宙学巡天的发展，通过针对最优探针，也可以为超越$\Lambda$CDM模型的共同现象学方面提供理论见解。