Sparsification of reduced order models for fluid and fluid-structure problems

复杂工程问题的数值模拟已成为航天系统高效设计和分析的重要步骤之一。然而，由于这些大规模动力系统的物理和计算模型的复杂性，计算成本可能是令人望而却步的。因此，无法解释或利用高效算法的预测模型和控制方案的成功非常有限。这个博士项目提出的中心问题是：我们能否开发一种稀疏互连的降阶模型，将数据驱动学习与基于物理的非线性降阶建模技术相结合？博士项目建立在达荣奇博士为耦合、非线性系统开发的方法学基础上。由此得到的非线性降阶模型包含一个二次张量，其大小随着所选模式的立方体而增长。总体思想是开发一个既是模型驱动又是数据驱动的框架，以提取降阶模型的紧凑、简化表示。模型的稀疏性特征通过识别相关交互的适当机器学习算法最大化。这项工作将考虑流体和流体结构问题。成功的申请者将被鼓励进一步发展分析和计算技能，与团队成员密切合作，并将研究成果提交给高质量的期刊。申请人还应在整个博士课程期间访问一所或多所海外机构。经过三年的学习，成功的申请者将利用作为研究项目一部分建立的人脉网络，为从事有回报的行业或学术生涯做好充分准备。

Numerical modelling of complex engineering problems has become one of the most important steps in efficient design and analysis of aerospace systems. However, due to the complexity of the physics and the computational modelling of these large-scale dynamical systems, computational costs may be prohibitive. Consequently, predictive models and control schemes that cannot account for or take advantage of efficient algorithms have very limited success. The central question posed in this PhD project is: Can we develop a sparsely-interconnected reduced order model, combining data-driven learning with a physics-based nonlinear reduced order modelling technique? The PhD project builds on the methodology developed by Dr Da Ronch for coupled, non-linear systems. The resulting nonlinear reduced order model contains a quadratic tensor, with size growing as the cube of the selected modes. The overarching idea is to develop a framework, which is both model- and data-driven, to extract a compact, reduced representation of the reduced order model. Sparsity features of the model are maximised by appropriate machine learning algorithms that identify the relevant interactions. The work will consider fluid and fluid-structure problems.The successful applicant will be encouraged to further develop analytical and computational skills, work closely with team members, and submit the research results to high-quality journals. The applicant is also expected to visit one or more overseas institutions throughout the duration of the PhD programme. After three years of study, the successful applicant will be well-prepared for a rewarding industrial or academic career, leveraging on the network of contacts created as part of the research project.