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Accelerated Large-Eddy Simulation via Universal Partial Differential Equations

Part of MS46 Differentiable Programming and Adjoint Methods in the Geosciences Accelerated Large-Eddy Simulation via Universal Partial Differential Equations Universal differential equation approaches directly mix neural networks and differential equation solving together in order to solve functional inverse problems in an efficient manner. In this talk we will discuss how universal partial differential equations (UPDEs) are being used to automate the process of developing parameterizations of the Boussinesq-approximated Navier Stokes equations for large-eddy simulations. This quasi-analytical approach uses a partial derivation to uncover a one-dimensional approximating PDE for the 3-dimensional dynamics, with a missing nonlocal operator. This nonlocal operator is approximated by training a neural network on numerical simulations generated via Oceananigans.jl in a way that is parameterized on the physical parameters of the fluid. The resulting surrogate is shown to be orders of magnitude faster than direct numerical simulation while being valid over a large range of physical quantities. We will end by describing the efforts that are being undertaken to validate these UPDE-based parameterizations within the Clima global circulation model. Christopher V. Rackauckas, Massachusetts Institute of Technology, U.S., [email protected] Related links: https://sciml.ai/ https://arxiv.org/abs/2010.12559 https://arxiv.org/abs/2001.04385