Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of the dynamics to which they give rise. In this work we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of non-linear dynamics, which we demonstrate by learning an entire cost matrix for a non-linear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.

翻译：网络结构是许多复杂现象动力学的基础，从基因调控和食物网到电网和社交媒体。然而，由于这些结构通常无法直接观测，必须通过观察其产生的动力学行为来推断连接关系。本研究提出了一种强大的计算方法，利用神经网络从时间序列数据推断大型网络邻接矩阵，并通过反映推断问题欠定性程度及数据噪声的方式，为预测提供不确定性量化。这是其他方法迄今所缺乏的功能。我们通过推断英国电网对停电事件的线路故障位置来展示该方法的能力，为每条边提供概率密度，并允许使用假设检验对故障位置做出有意义的概率性陈述。在噪声数据及问题欠定情况下，我们的方法显著优于马尔可夫链蒙特卡洛采样和最小二乘回归，同时自然扩展到非线性动力学情形——我们通过为大伦敦地区非线性经济活动模型学习完整成本矩阵来证明这一点。该方法并非专为网络推断设计，实际上它代表了一种适用于任意高维参数空间的通用参数估计方案。