A New Framework for Nonlinear Dynamical Model Reduction

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The research objective of this project is to apply multivariate and nonlinear time series analyses in formulating comprehensive and systematic dynamical model and data reduction framework. In this framework, smooth orthogonal decomposition will be applied to the dimension reduction of deterministic nonlinear dynamical systems and will be contrasted with other alternatives - e.g., proper orthogonal decomposition. The research approach is to test the framework on several large-scale structural and molecular dynamics models' short time trajectories, and evaluate the resultant subspaces suitability for model reduction. Reduced-order models based on these subspaces will be simulated and compared with the full-scale models, using frequency response functions, bifurcation diagrams, phase portraits, and other dynamical characteristics such as fractal dimensions and Liapunov exponents.This framework will provide a systematic way of evaluating a particular model reduction procedure's effectiveness and its robustness with respect to the bounded variations in the system/forcing parameters, and initial conditions. This project is expected to provide new tools to study slow-time dynamics of complex engineered and biological systems (e.g., physics of protein conformational changes or folding, protein-protein association, large multi-physics dynamics, etc.). For a protein system, e.g., this methodology can be exploited in the rational design of next generation compound-antagonists. The plan also supports the curricular expansion of two interdisciplinary graduate courses, the organization of department-wide workshops on graduate research for junior and senior students, the regular organization of conferences and minisymposia, the dissemination of results through the web, personal communication, and traditional publications in top journals.