Multiscale modelling of systems with complex microscale detail

在现代科学和工程中，许多复杂系统是用不同空间区域内明显不同的微观物理模型来描述的。该项目旨在发展系统的数学和计算方法，以便为工业研究和发展中应用的此类系统建立紧凑而精确的宏观模型和计算。我们的稀疏模拟，通过数学分析证明，使用粒子/代理模拟，偏微分方程或差分方程的小爆发，有效地评估宏观尺度系统级行为。目标是准确地连接不同的微尺度模型，并建立关于微观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.