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Applied Math Seminar

November 12, 2021 - 3:00pm

COB2 170

Speaker: Yuanran Zhu

Title: Reduced-order modeling for the high-dimensional dynamical system: Methodologies and applications

Abstract: Modern computational hardware enables us to perform large-scale simulations for complex systems ranging from turbulence to the molecular dynamics model for proteins with million atoms. These dynamical systems are usually high-dimensional and the exact simulation to capture the physics of the entire system on a long-timescale can be infeasible due to the curse of dimensionality. In practice, however, it is often the case that only some low-dimensional observables of a large system are particularly important for research. Typical examples are the movement of a characteristic Lagrangian particle in fully developed turbulence and the active site of an enzyme where substrate molecules bind and undergo a chemical reaction. This necessitates the development of theoretical and computational strategies to construct effective or coarse-grained models that describe the dynamics of these reduced-order quantities. In this seminar, I will introduce several first-principle and data-driven methods for reduced-order modeling and their applications to turbulent dispersion, far-from-equilibrium heat conduction, rare-event calculations, and other physical problems. Through the relevant discussion, we would like to show that these methodologies not only provide novel computational strategies for the dimension-reduction of high-dimensional deterministic and stochastic systems but also introduce new paradigms to discover hidden physical laws.