发表机构
Stanford University; Kavli Institute for Particle Astrophysics and Cosmology; Leinweber Institute for Theoretical Physics（斯坦福大学; 卡弗里粒子天体物理与宇宙学研究所; 莱因韦伯理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出拉格朗日神经细胞自动机（LNCA），以混合深度学习框架模拟宇宙结构形成，实现了非线性区域的高保真模拟，参数远少于同类模型，可作为重建宇宙初始条件的可靠可微正向模型。
AI 中文摘要
从星系巡天数据推断宇宙学初始条件的场级任务，需要一个同时具备非线性区域精度高、计算效率高且完全可微的正向模型。传统N体模拟精度高，但迭代推断时计算成本过高；而拉格朗日微扰理论（LPT）这类近似求解器，无法捕捉宇宙网后期形成暗物质晕的复杂动力学。我们提出拉格朗日神经细胞自动机（Lagrangian Neural Cellular Automaton, LNCA），这是一种混合深度学习框架，可将结构形成模拟为共动格点上的局部迭代动力学过程。与映射固定密度场的标准欧拉卷积神经网络（CNN）不同，LNCA在拉格朗日框架下运行，通过平移计算图本身来跟随质量流动。我们仅训练网络学习泽尔多维奇近似（Zeldovich approximation）的残差位移修正，从而在保证大尺度精度的同时，实现非线性物理的高保真模拟。我们还通过采用等变细胞自动机架构约束模型，使其生成完整轨迹而非仅最终状态，该架构会循环迭代内部状态以产生动态演化历史。最终得到的模型具有严格局部性、平移和旋转等变性，且天然支持连续时间积分，是从光锥数据重建宇宙初始条件的可靠可微正向模型。我们训练的模型在非线性区域（$k \thinspace \text{Mpc}^{-1}$）的功率谱和交叉谱达到百分位精度，且参数数量仅为采用可解释内部动态规则集的同类模型的约10^4分之一。
英文摘要
Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable. Traditional N-body simulations are accurate but computationally prohibitive for iterative inference, while approximate solvers like Lagrangian Perturbation Theory (LPT) fail to capture the knotty halo-forming dynamics of the cosmic web at late times. We introduce the \textit{Lagrangian Neural Cellular Automaton} (LNCA), a hybrid deep learning framework that can be applied to emulate structure formation as a local, iterative dynamical process on a comoving lattice. Unlike convolutional emulators which map fixed grids in a single pass, the LNCA operates in the Lagrangian frame, iteratively advecting the computational graph itself to follow the flow of mass. By training the network to learn only the \textit{residual} displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics while guaranteeing accuracy at large scales. We further constrain our model to produce complete trajectories, not just final states, by adopting an equivariant cellular automaton architecture, which recurrently iterates on its internal states to yield a dynamic history. The resulting update rule acts on a single fixed neighborhood, is translationally and rotationally equivariant, and is integrated over discrete substeps to yield trajectories, making it a differentiable forward model for reconstructing the initial conditions of the universe from lightcone data. We train our model to emulate the real-space matter distributions of a diverse set of N-body simulations from the Quijote suite, for a range of redshifts and cosmologies, given only the initial conditions.
