Interface-aware numerical methods for stochastic inverse problems

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This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multilevel methods, transport maps, and dimension reduction, this project's anticipated outcomes are highly accurate and cost-efficient numerical schemes, certified by rigorous mathematical analysis. This should provide data-centric simulation tools with enhanced reliability, for engineering and scientific applications.