Data-Driven Reduced-Order Modeling of Ab Initio Molecular Dynamics

现代材料科学、化学和细胞生物学中的许多问题都涉及到外加电场在微观水平上的结构变化。定量描述必须考虑到潜在的电子结构和诱导的原子运动，这导致了复杂的、大维度的动力学系统，对于这些系统，直接模拟是昂贵的。该项目通过开发有效的数学模型来显著降低计算成本，从而解决了这一根本的实际困难。这一缩减还使这些模型能够应用于具有直接实际意义的大得多的系统。该项目还为研究生提供了研究培训机会。该项目旨在开发从头计算框架内的降阶建模技术。这样做的目的是避免重复计算电子结构，从而大大加快整体计算速度。作为Galerkin投影的形式，这些技术将电子动力学投影到自由度要少得多的子空间，同时仍然保留了外场与分子和原子动力学之间的重要映射。提出了一种统计方法，以便当模型可用时，从包含原子轨迹的数据集中推断模型。该项目还包括对具有复杂组成和生物系统电学性质的材料的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Many problems in modern material science, chemistry, and cell biology involve the structural changes at the microscopic level driven by external electrical fields. A quantitative description must take into account the underlying electronic structures and the induced atomic motions, leading to complex, large-dimensional dynamical systems, for which direct simulations are expensive. This project tackles this fundamental practical difficulty by developing efficient mathematical models to significantly reduce the computational cost. The reduction also enables the application of these models to much larger systems that are of direct practical interest. The project also provides research training opportunities for graduate students.This project aims to develop reduced-order modeling techniques within the framework of ab initio calculations. The goal is to avoid repeated calculations of the electronic structures so that the overall computation can be drastically sped up. Formulated as a Galerkin projection, the techniques project the electron dynamics to subspaces with much fewer degrees of freedom, while still retaining the important mapping between the external field and the dynamics of molecules and atoms. A statistical approach is proposed so that the models be inferred from a dataset containing atomic trajectories whenever they are available. This project also includes applications to materials with complex compositions and electrical properties of biological systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.