LDHD in Chemistry and Chemical Engineering
The research projects are (1) reduced order modeling for quantum chemistry computations using sparse grids and (2) identification of inertial manifolds and/or fast and slow time scales for dynamic with black-box or equation-free forcing terms.
The objective of project 1 is to simulate changes in the configuration of a molecule, for example when exited by light. We will model the dynamics by evaluating the energy at a well-chosen set of nodes in a subspace of configuration space and then driving the dynamics with the gradient of the model. The two phases of model reduction are (a) selection of a good and small set of configuration variables and (b) building the interpolatory model. Without (b) the computation would be impossible, as it would require driving dynamics by differentiating the output of a chemistry code (with no access to source).
Project 2 uses matrix-free Krylov subspace methods to identify low dimensional inertial manifolds in cases where the dynamics are not explicitly given by formulae. Examples include using black-box legacy codes or the outputs of upscaled microscale simulations.
Reaction Path Following with Sparse Interpolation
MOLECULAR POTENTIAL ENERGY SURFACE APPROXIMATION AND REACTION PATH FOLLOWING WITH SPARSE INTERPOLATION
Investigating Molecular Transformations with Sparse Interpolatory Models
Surrogate Models: Investigating Molecular Dynamics with Smolyak’s Sparse Interpolation Algorithm
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Carl Kelley