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.
|Effective start/end date||9/1/20 → 8/31/23|
- National Science Foundation: $120,000.00