Physics-constrained adaptive learning for multi-physics optimization: Time-accurate prediction of chaotic and turbulent flows

流体力学模型预测流动演变的能力既有物理原理，也有经验方法。一方面，物理原理(例如守恒定律)是外推的--它们提供了对尚未观察到的现象的预测。另一方面，经验模型提供了数据内的相关函数。人工智能和机器学习在经验建模方面表现出色。在这个项目中，学生将把物理原理和经验模型结合到一个统一的方法中：物理约束的数据驱动方法，用于多物理优化。目标是在机器学习中约束湍流的控制方程。这将实现更高的准确性、健壮性和通用性。

The ability of fluid mechanics modelling to predict the evolution of a flow is enabled both by physical principles and empirical approaches. On the one hand, physical principles (for example conservation laws) are extrapolative - they provide predictions on phenomena that have not been observed. On the other hand, empirical modelling provides correlation functions within data. Artificial intelligence and machine learning are excellent at empirical modelling. In this project, the student will combine physical principles and empirical modelling into a unified approach: physics-constrained data-driven methods for multi-physics optimisation. The objectives are to constrain the governing equations of turbulence in machine learning. This will enable more accuracy, robustness, and generalization.