Abstract
We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead.
Highlights
The growing advancements in computational power, technological breakthrough, algorithmic innovation, and the availability of data resources have started shaping the way we model physical problems and for years to come
The parameter η gives us a freedom to benefit from both modeling techniques mentioned above rather than fully depending on a single modeling technique, and, as we show in Section 6, the hybrid model with optimal contribution from both modeling approaches gives a better prediction of the true solution than the individual modeling approaches
We propose a reliable and robust reduced-order modeling technique using a hybrid framework
Summary
The growing advancements in computational power, technological breakthrough, algorithmic innovation, and the availability of data resources have started shaping the way we model physical problems and for years to come. Many of these physical phenomena, whether it be in natural sciences and engineering disciplines or social sciences, are described by a set of ordinary differential equations (ODEs) or partial differential equations (PDEs) which is referred as the mathematical model of a physical system. These techniques require parameter calibration to approximate the true solution to any degree of confidence and may increase costs related to model validation and benchmark data generation
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