Learning subgrid-scale models with neural ordinary differential equations

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by method of lines and their representation in chaotic ordinary equations, based on neural (NODEs). Solving systems with fine temporal spatial grid scales is an ongoing computational challenge, closure models are generally difficult tune. Machine approaches have increased accuracy efficiency fluid dynamics solvers. In this networks used learn coarse- fine-grid map, which can be viewed as parameterization. strategy that uses NODE knowledge source at continuous level. Our inherits advantages NODEs parameterize subgrid scales, approximate coupling operators, improve low-order Numerical results two-scale Lorenz 96 ODE, convection–diffusion PDE, viscous Burgers’ PDE illustrate approach.