Model Reduction for High-dimensional Stochastic Non-linear Dynamical Systems: The Devil in the Details

Abstract: Non-convex stochastic dynamical systems such as those which describe the statistical mechanics of crystal formation, solvation, and macromolecular dynamics in liquid state suffer from the curses of dimensionality and also of highly rugged landscapes. Many efforts have been made to develop algorithms that attempt to determine reduced representations and kinetically-slow variables for these high dimensional systems from simulation. Molecular dynamics simulations can provide the numerical experiments for applying these algorithms, and also offer atomic-level dynamical information important for understanding mechanisms that drive essential condensed matter phenomena. Supercomputers and high-performing and accelerated simulation programs, together with sophisticated ensemble methods, have pushed simulations to unprecedented levels, however, accuracy of the models continues to suffer. In addition, the problem of determining the correct reduced representation accurately remains unsolved. I will discuss the state-of-the art in model reduction methods for molecular dynamics simulations and our efforts to create HPC-based programs that can implement one of these, the Markov state model, along with recent results indicating that the intuitively-derived, traditionally accepted features chosen for reduced representations may be highly incomplete. I will conclude with a presentation of new directions we are proposing to address these problems.

Bio: Dr. Ada Sedova is an R&D staff member working in the Biophysics Group at the Oak Ridge National Laboratory. Ada was a CSEEN Postdoctoral Research Associate in the Scientific Computing Group at NCCS, ORNL, and in the Department of Chemistry, University at Albany. She received her PhD in Biomedical Sciences with focuses on computational biophysics, biophysical chemistry and structural bioinformatics from the joint program at the NY State Department of Health/Wadsworth Center–University at Albany’s Biomedical Sciences Department. She also received a Masters in Mathematics from the University at Albany’s Department of Mathematics and Statistics with a research focus on stochastic processes in physics and chemistry. Her work focuses on condensed matter chemical physics, including structure and dynamics of biomolecules, non-covalent interactions and supramolecular assemblies, and statistical mechanics of condensed matter systems,along with genomics and bioinformatics. This includes computational work using high-performance scientific computing programs for simulation and analysis, and experimental work including neutron scattering, biophysical chemistry and electrochemistry.