Recent advances in computational resources and the development of high-throughput frameworks enable the efficient sampling of complicated multivariate functions. This includes energy and electronic property landscapes of inorganic, organic, biomolecular, and hybrid materials and functional nanostructures. Combined with the recent focus on data science and the materials genome initiative, this leads to a rapidly growing need for numerical methods and a fundamental mathematical understanding of efficient sampling approaches, optimization techniques, hierarchical surrogate models and coarse graining techniques, and methods for uncertainty quantification.
The complexity of these energy and property landscapes originates from their simultaneous dependence on discrete degrees of freedom (e.g. number of atoms and species types) and continuous ones (e.g. position of atoms). The complexity is further exacerbated by the presence of divergences (e.g. when atoms approach one another and at critical transition points) and non-trivial emergent phenomena that are due to collective interactions. Moreover, dynamical behavior governed by complex landscapes involves a rich hierarchy of timescales and is characterized by rare events that often are key to understanding function of the molecular structures under investigation. This complexity provides an ideal test bed for novel mathematical methods that characterize these functions and provide a description as well as optimal numerical methods.
This program will bring together researchers from pure and applied mathematics, computer science, materials science, chemistry, physics, and biomolecular science to advance the understanding of simulation, stochastic sampling and optimization methods for multidimensional energy landscapes and to develop a common language.
(Rice University, Physics)
Graeme Henkelman (University of Texas at Austin)
Richard Hennig (University of Florida)
Tony Lelièvre (Ecole des Ponts ParisTech)
Mitchell Luskin (University of Minnesota, Twin Cities, School of Mathematics)
Noa Marom (Carnegie-Mellon University, Physics and Engineering Physics)
Petr Plechac (University of Delaware)
Christof Schuette (Freie Universität Berlin)