Interface-aware numerical methods for stochastic inverse problems

本项目旨在设计新型高性能数值工具，用于求解随机界面主导的大规模正、逆问题和量化相关不确定性。在地下水等实际应用中，这些工具有助于将大数据集吸收到数学模型中，从而提供可靠的预测。通过推进和整合高阶多面体方案、多层方法、运输图和降维，本项目的预期成果是高度精确和具有成本效益的数值方案，并经过严格的数学分析验证。这将为工程和科学应用提供具有增强可靠性的以数据为中心的仿真工具。

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.