Faster and cheaper cosmological data analysis thanks to a physics-driven machine learning strategy

宇宙学社区在计算集群上大规模运行爱因斯坦-玻尔兹曼解算器，以从大尺度结构和宇宙微波背景数据推断宇宙学参数。这些代码的任何显著加速都将导致显着的效率提高和计算成本节省。尽管正在努力以最佳方式重新制定这些代码的某些部分，但这些代码仍然存在一个瓶颈：描述问题中几个最大波数的宇宙学扰动演化的微分方程系统的集成。这不能通过巧妙的并行化方案来缩小规模。我们建议用经过训练的神经网络来代替这个瓶颈。我们的策略比以前的尝试更通用，因为神经网络只会取代一个中间步骤，这只取决于减少的模型参数（而不是与精确实验相关的特定可观察量相关的任何参数）。我们将用物理驱动的策略来解决这个问题。我们将使用宇宙微扰理论的半解析结果来指导非常有效的网络的设计，其中可以用小的训练集实现良好的精度。我们将发布一个模块，可以与任何爱因斯坦-玻尔兹曼求解器接口，以加快它们的速度。我们还将调整参数推断代码的结构，以便在参数提取运行期间充分利用这种加速，即使考虑超出先前现有训练集的模型。最后，我们将建立一个全球战略，以避免在全球宇宙学界重复运行。通过建立公共存储库并在参数推断代码中添加一些通信模块，我们将确保训练集和神经网络的有效性范围随时间而增长，而不会为任何组产生任何额外的计算负载，甚至不会为托管中央存储库的组产生任何额外的计算负载。该计划可以在全球范围内带来巨大的效率提升和资金节省。我们估计，由于这个项目，宇宙学社区每年可以节省10亿CPU小时的数量级，我们的整体策略可以在其他领域复制。我们将说明各种宇宙学数据分析（参数推断和灵敏度预测）的新方法的性能，我们将建议实施它的管道中的一些合作，如欧几里得。

The community of cosmology massively runs Einstein-Boltzmann solvers on computing clusters in the context of cosmological parameter inference from Large Scale Structure and Cosmic Microwave Background data. Any significant speed-up of these codes would result in dramatic efficiency gains and computational cost savings. Despite of on-going effort to reformulate some parts of these codes optimally, these codes still have one bottleneck: the integration of the system of differential equations describing the evolution of cosmological perturbations for the few largest wavenumbers in the problem. This cannot be scaled down by clever parallelisation schemes. We propose to replace this bottleneck by trained neural networks. Our strategy is more universal than previous attempts, because the neutral networks will only replace one intermediate step, that depends only on a reduced number of model parameters (and not on any parameter related to a particular observable related to a precise experiment). We will approach the problem with a physics-driven strategy. We will use semi-analytical results on cosmological perturbation theory to guide the design of very efficient networks, in which good precision can be achieved with small training sets. We will release a module that can be interfaced with any Einstein-Boltzmann solver to speed them up. We will also tweak the structure of parameter inference codes in order to take full advantage of this speed up during parameter extraction runs, even when models beyond the previously existing training set are considered. Finally we will set up a global strategy to avoid duplicate runs throughout the worldwide cosmology community. By setting up public repositories and adding some communication modules in parameter inference codes, we will ensure that the range of validity of the training set and of the neural networks grows with time without generating any extra computing load for any group, not even the group hosting the central repository. This scheme can lead to massive efficiency gains and money savings worldwide. We estimate that the cosmology community could save of the order of a billion CPU-hours every year thanks to this project, and our overall strategy could be replicated in other fields. We will illustrate the performances of the new approach in various cosmological data analysis (parameter inference and sensitivity forecasts) and we will propose to implement it in the pipelines of some collaborations like Euclid.