随机复杂系统在生物化学、环境学以及气候预报等实际问题中有着广泛的应用和研究背景，这类复杂系统的数学模型都是建立在多个不同尺度的时间和空间范围内。利用多尺度数值方法来研究随机复杂系统时，需要注意两方面的问题，一方面宏观模型和微观模拟信息交换时，会缺失一些统计信息，另一方面其数值模型缺乏有效的快速算子。为更好的处理上述问题，我们拟研究：（1）提出一个新随机杂交算法，从而促进宏观模型和微观模型的信息交换；（2）利用自适应基多元广义多项式混沌技术，构造一个求解随机偏微分方程的新的快速算子，从而加速正问题的求解，进而给出一个解决随机复杂系统的快速高效算法。这些理论与数值计算方法的研究将改变人们对随机复杂系统中相关现象的认识，在应用中有着重要的实用价值和现实意义。

Stochastic complex systems are widely seen in many practical problems,such as biochemistry, environmental science, climatological forecast etc. There are two major limitations in multiscale modeling of complex systems: (1) the loss of crucial statistical information when datum exchanges between the macroscale model and mesoscale simulation, and (2) lack of efficient numerical solvers. To overcome these difficulties, we propose two solutions: (1) to develop a new stochastic hybrid algorithm which makes the datum exchange between macroscale model and mesoscale simulation be more efficient; (2) to develop an efficient algorithm for solving stochastic partial differential equations (SPDEs). A successful completion of the research shall accelerate the solving of forward problems, which provides a fast and efficient numerical solver for stochastic complex system. The proposed theoretical and computational research will significantly strengthen our ability in dealing with challenging issues within stochastic complex systems, which is valuable and has long lasting impact in advancing science and technology.