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This paper introduces a machine learning method for creating subgrid-scale (SGS) parameterizations in coarse simulations of the Burgers' equation by leveraging structure-preserving neural networks and entropy variables. The authors implement a decoupled neural network architecture that separates subgrid corrections into a conservative Flux Potential network and an Eddy Viscosity network, ensuring high fidelity in reproducing key physical characteristics of the full-scale system. The results demonstrate that this reduced-order framework not only accurately captures the energy spectrum and correlation functions but also remains robust across parameters beyond the training regime.
Achieving high physical fidelity in coarse simulations of the Burgers' equation through a novel decoupled neural network architecture that separates subgrid corrections.
We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers'equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.
