2 - Topology

3 - Prediction

Animation:** Principle component analysis of the hexagonal roaming landscape of the K+ cation about Al(OH)4- in water.** The black path depicts an effective path for K+ to move from one O to another O site, with the direction governed by three PC vectors as shown in the figure on the right panel.

Many topological data analysis tools require data with a small number of dimensions, but raw chemical energy landscapes tend to naturally have very large dimensions: 3N for N atoms. The primary goal of thrust 1 is to investigate techniques that can reduce the dimensionality of chemical energy landscapes, such as those from molecular dynamics simulations, while preserving topology. Using simulations of model chemical reactions, thrust 1 will investigate statistical methods like principal component analysis, diffusion map and active subspace, as well as nonlinear manifold learning techniques such as Isomap and Umap, to extract a low-dimensional subspace of the chemical energy landscape. Applying topological analysis tools from thrust 2 to a sequence of reduced energy landscapes will be used to determine the extent of "dimensional compression" achievable by each technique. Additionally, thrust 1 will also investigate topological descriptors such as chemical reaction networks, social permutation invariant and PageRank as collective variables that reduce the dimensionality of the energy landscape. As above, applying topological data analysis tools to data projected onto various combinations of collective variables will determine the capability of preserving chemical energy landscape topology within spaces of lowest possible dimension.

Thrust 1 Team Lead:

**Ravishankar Sundararaman**, Assistant Professor, Materials Science and Engineering, Rensselaer Polytechnic Institute