While the evolution of linear initial conditions present in the early universe into extended halos of dark matter at late times can be computed using cosmological simulations, a theoretical understanding of this complex process remains elusive. Here, we build a deep learning framework to learn this non-linear relationship, and develop techniques to physically interpret the learnt mapping. A three-dimensional convolutional neural network (CNN) is trained to predict the mass of dark matter halos from the initial conditions. We find no change in the predictive accuracy of the model if we retrain the model removing anisotropic information from the inputs. This suggests that the features learnt by the CNN are equivalent to spherical averages over the initial conditions. Our results indicate that interpretable deep learning frameworks can provide a powerful tool for extracting insight into cosmological structure formation.

翻译：虽然早期宇宙中存在的线性初始条件在后期演变成深物质大洞,可以通过宇宙模拟来计算,但对这一复杂过程的理论理解仍然难以实现。 在这里,我们建立了一个深层次学习框架来学习这种非线性关系,并开发了对所学绘图进行物理解释的技术。一个三维进化神经网络(CNN)经过培训,从最初的条件中预测暗物质大洞的质量。如果我们重新将模型从输入中去除厌食信息,我们发现模型的预测准确性没有变化。这表明CNN所学的特征相当于初步条件的球状平均数。我们的结果显示,可解释的深层学习框架可以提供强大的工具,用于对宇宙结构形成进行洞察。