The project aims to develop novel methodologies to improve model predictions and guide intervention measures in response to increasing risks of disease spread and cascade failure. We address the modeling challenges posed by large networks and integrate ideas from machine learning and stochastic modeling to enable efficient yet highly accurate predictions of complex network dynamics. Machine learning methods have emerged as powerful tools with the potential to deal with the challenges of increasing complexity. However, purely data-driven approaches remain tied to problems for which huge data sets are accessible. In contrast, high-dimensional and dynamic networks often lack sufficiently large data sets to rely on a purely data science approach.

The model reduction techniques developed for real-world networks can play a crucial role in merging mechanistic and data-driven approaches by providing a sufficiently accurate yet computationally affordable description of complex phenomena. By pursuing a work plan for such model data fusion, we aim to develop data-driven reduced stochastic models. In addition to questions of scientific computing in areas of uncertainty quantification and the optimal design of stochastic networks, such techniques have overarching applications from the development of digital twins to human mobility modeling, and to fake news detection.

Kinetic interactions of particles comprise challenging problems across different fronts of modelling, computation and analysis of fluids. From hypersonic and reentry flights to the high-energy chip lithography and membranes, we rely on kinetic descriptions to elucidate the underlying meso-scale transport processes. As the flow condition departs noticeably from thermal equilibrium, the accuracy of conventional, linear-response-type closures deteriorates.  In the past decade, continuous stochastic models governed by the Fokker-Planck equation were investigated as a novel strategy to construct meso-scale models honouring the physical constraints of nonequilibrium flows. Many crucial pieces are still missing to reach a general-purpose computational framework. In particular, real gas complexities arising from internal degrees-of-freedom hinder Fokker-Planck approximation of polyatomic kinetics. Moreover, an adaptive and cascade type rationale needs to be developed in order to equip us with appropriate means to reach the full capability of the Fokker-Planck model, both in terms of accuracy and efficiency.

The central idea of this project is to bring together a mathematically well-defined polyatomic Boltzmann equation and its corresponding hierarchical Fokker-Planck approximations. The outcome gives us a numerical toolbox appropriate for studying complex gas transport processes through mesoporous membranes, with overarching applications in gas separation and CO2 adsorption.