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Center for Nonlinear Studies |
Diffusion processes are widely used to model complex phenomena, e.g. in finance, climate research, or in molecular dynamics simulations of biomolecules. Simulating these systems at full resolution is often prohibitively costly and results in huge amounts of data that are difficult to analyze. Recently, a systematic way of obtaining effective dynamics on reduced coordinates has been proposed in Lelièvre et al, Nonlinearity, 2010. The coordinates can be any smooth transformation of the original state space, and the dynamics are obtained as averages over level sets of the transformation. Here, we present theoretical and numerical results on the approximation quality of the effective dynamics for reversible diffusions. We also discuss parameter estimation for the effective dynamics from simulation data of the original process, and show how physical interpretability of the parameters can be enforced using additional sparsity constraints.
Host: Danny Perez