Multiscale modelling of systems with complex microscale detail

在现代科学和工程中，许多复杂系统在不同的空间区域内由明显不同的微尺度物理模型描述。该项目旨在为此类系统的紧凑和准确的宏观建模和计算开发系统的数学和计算方法，以应用于工业研究和开发。我们的稀疏模拟，合理的数学分析，使用粒子/代理模拟，偏微分方程，或差分方程的小突发，有效地评估宏观系统级的行为。目标是在不同的微尺度模型之间精确地接口，并建立关于微尺度参数空间如何在宏观尺度上解决的可证明的预测。

In modern science and engineering many complex systems are described by distinctly different microscale physical models within different regions of space. This project is to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling and computation of such systems for application in industrial research and development. Our sparse simulations, justified with mathematical analysis, use small bursts of particle/agent simulations, PDEs, or difference equations, to efficiently evaluate macroscale system-level behaviour. The objective is to accurately interface between disparate microscale models and establish provable predictions on how the microscale parameter spaces resolve at the macroscale.