Using a set of ΛCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams’ development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web’s hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

The Groningen gas field in the Netherlands is experiencing induced seismicity as a result of ongoing depletion. The physical mechanisms that control seismicity have been studied through rock mechanical experiments and combined physical-statistical models to support development of a framework to forecast induced-seismicity risks. To investigate whether machine learning techniques such as Random Forests and Support Vector Machines bring new insights into forecasts of induced seismicity rates in space and time, a pipeline is designed that extends time-series analysis methods to a spatiotemporal framework with a factorial setup, which allows probing a large parameter space of plausible modelling assumptions, followed by a statistical meta-analysis to account for the intrinsic uncertainties in subsurface data and to ensure statistical significance and robustness of results. The pipeline includes model validation using e.g. likelihood ratio tests against average depletion thickness and strain thickness baselines to establish whether the models have statistically significant forecasting power. The methodology is applied to forecast seismicity for two distinctly different gas production scenarios. Results show that seismicity forecasts generated using Support Vector Machines significantly outperform beforementioned baselines. Forecasts from the method hint at decreasing seismicity rates within the next 5 years, in a conservative production scenario, and no such decrease in a higher depletion scenario, although due to the small effective sample size no statistically solid statement of this kind can be made. The presented approach can be used to make forecasts beyond the investigated 5-years period, although this requires addition of limited physics-based constraints to avoid unphysical forecasts.