Multi-scale description of multi-phase fluid flows using data-driven closures

如何准确地描述多相流体的流动，并结合有效的数值方法，一直是科学计算领域的挑战之一。本研究计划的目标是设计一个连续体模型，该模型部署基于潜在分子相互作用的数据驱动的中尺度闭包。特别地，考虑由Enskog-Vlasov动力学方程产生的力矩方程，守恒定律中的未闭项可以用守恒量的力矩及其空间导数来建模。一旦利用了解空间的适当基函数，闭包问题就转化为一个回归问题，即找到与分子相互作用相关的项的投影系数，并给定感兴趣点周围的力矩。在这里，一个有效的高维回归模型从机器学习文献，如人工神经网络适用于关闭问题将部署和离线训练。训练数据集将通过在适用范围的边界条件的参考配置中执行蒙特卡罗中尺度模拟来生成。最后，将训练好的多尺度解算法作为目标测试用例，在相应的模拟环境中对平流层气溶胶的演化进行研究。因此，本研究计划旨在为流体流动的大规模模拟提供一个高效、准确和灵活的框架，该框架允许使用高效的高维回归方法将微尺度物理一致地包含在经典守恒定律中。申请人选择麻省理工学院（MIT）的Nicolas G. Hadjiconstantinou教授作为博士后研究的负责人，因为他在动力学理论和多尺度建模中的方差减少蒙特卡罗方法方面进行了广泛的研究和相关贡献。此外，麻省理工学院的Youssef Marzouk教授是贝叶斯推理和不确定性量化方面的专家，他将支持申请人设计一个与本研究计划相关的可靠回归模型。

An accurate description of multi-phase fluid flows that is accompanied with an efficient numerical method remains one of the challenges in the realm of scientific computing. The target of this research proposal is to devise a continuum model that deploys data-driven mesoscale closures based on underlying molecular interactions. In particular, considering moment equations resulting from the Enskog-Vlasov kinetic equation, the unclosed terms in the conservation laws can be modeled using the moments of conserved quantities and their spatial derivatives. Once an appropriate basis function for solution space is utilized, the closure problem converts to a regression problem of finding the projected coefficients for terms associated with molecular interactions given the moments around the point of interest. Here, an efficient high dimensional regression model from Machine Learning literature such as Artificial Neural Network suitable for the closure problem will be deployed and trained offline. The training data set will be generated by performing Monte Carlo mesoscale simulations in a reference configuration for an applicable range of boundary conditions. Finally, as the target test case, the trained multi-scale solution algorithm will be tested by studying the evolution of Stratospheric aerosols in a relevant simulation setting. As the outcome, this research proposal intends to provide an efficient, accurate, and flexible framework for large scale simulations of fluid flows that allows consistent inclusion of micro-scale physics in the classical conservation laws using efficient high dimensional regression methods.The applicant has chosen Prof. Nicolas G. Hadjiconstantinou at Massachusetts Institute of Technology (MIT) to be the host for this postdoctoral study, because of his extensive research and relevant contributions for variance-reduction Monte Carlo methods in kinetic theory as well as multi-scale modeling. Furthermore, Prof. Youssef Marzouk at MIT, who is an expert in Bayesian inference and uncertainty quantification, will support the applicant with devising a reliable regression model relevant for this research proposal.