Neural operator-enabled closure for stochastically forced Burgers' equation.

Data-driven closure models based on supervised learning often fail to generalize in part because the neural networks are tied to a specific discretization. An alternative to alleviate this is to work within an operator learning framework. We present a data-driven closure for the stochastically forced Burgers' equation. Under this forcing, we show that the learned residual stress approximates the statistics related to DNS and compare against classical Smagorinsky-type closures. The resulting closure can generalize across (shock-less) conditions and grid sizes, the latter of which is enabled by leveraging Fourier neural operators (FNOs).