Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables

• URL: http://arxiv.org/abs/2607.14855v1
• Date: Thu, 16 Jul 2026 11:23:37 GMT
• Title: Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
• Abstract summary: We present a machine learning approach for developing subgrid-scale parametrizations in coarse simulations of partial differential equations.<n>We show that our approach is robust and applicable to parameters outside the training regime.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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