Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems

Many physical phenomena governed by nonlinear dynamics possess motions that occur on a wide range of timescales. Numerical solutions for such problems often require a large number of variables to achieve acceptable accuracy. When an insucient resolution is used to evolve a solution, an irreversible loss of information occurs, which can lead to substantial errors. Presented here is a novel method for optimal temporal reduced order modeling (OPTROM), which can be used to enhance the fidelity of any time domain solution technique. Statistical information about the unresolved variables, in the form of conditional expectations, is used to more accurately predict the evolution of the resolved variables. To demonstrate the OPTROM technique, harmonic balance solutions for a Dung oscillator are investigated. The need for, and ecacy of, the technique is greatest when solutions are obtained with a low resolution.

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