Ideas from multiscale geometric analysis of points clouds and diffusion geometry may be generalized to study data from molecular dynamics simulations, in particular to (1) estimate the number of effective degrees of freedom locally in state space, in a way that is robust to noise and requires a small number of samples, (2) estimate a local scale (in state space) where the system may be well-approximated by a local linear low-dimensional diffusion, and finally to (3) construct global nonlinear reactions coordinates for the system. We then estimate the local diffusion coefficients in the low-dimensional reduced space, and show that certain important large-time statistics (e.g. transition rates) are well-reproduced. Finally, we attempt a physical interpretation for the reduced system of coordinates. This is joint work with C. Clementi, M.A. Rohrdanz and W. Zheng.
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