Variational Principles in Conformation Dynamics - FU Berlin, FB MI

44 V. Summary and outlookV.1.2. Choice of basis functionsSo far, we have exclusively used Gaussian functions, and more or less guessed their shapeparameters from the energy function. Can we make a more precise statement about therelation between the shape of the basis functions and the approximation quality, and whatother types of functions can be used?V.1.3. Numerical stabilityWe will have to address sources of numerical instabilities involved in our computations. Asmentioned before, choosing basis functions which are either too uncorrelated or correlatedtoo much can lead to meaningless results. Can we find a way to quantify these instabilitiesand determine how they are related to the choice of functions?V.1.4. Importance of samplingThe method does not work without the computation of simulation trajectories. In the examplewe studied, it was easy to compute trajectories which visit all the metastable regionsfrequently often. But what does this mean for greater systems? How can we determinethe minimum length of a sufficiently long trajectory, and how much does the use of finitesimulations affect all the quantities involved in the method, like the H- andS-matrix?