We consider the problem of recovering equations of motion from multivariate time series of oscillators interacting on sparse networks. We reconstruct the network from an initial guess which can include expert knowledge about the system such as main motifs and hubs. When sparsity is taken into account the number of data points needed is drastically reduced when compared to the least squares technique. We show that the sparse solution is stable under basis extensions, that is, once the correct network topology is obtained, the result does not change if further motifs are considered.

中文翻译：

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恢复稀疏网络：扩展下的基础适应性和稳定性

我们考虑了从稀疏网络上相互作用的振荡器的多元时间序列中恢复运动方程的问题。我们从最初的猜测中重建网络，该猜测可以包括有关系统的专业知识，例如主要主题和集线器。当考虑稀疏性时，与最小二乘法相比，所需的数据点数将大大减少。我们表明，稀疏解在基本扩展下是稳定的，也就是说，一旦获得了正确的网络拓扑，如果考虑其他主题，结果就不会改变。