High-resolution simulations that fully resolve all spatiotemporal scales of geophysical and turbulent flows remain a challenge in large ocean domains. Large-eddy simulations (LES) make these computations tractable by filtering out subgrid-scale (SGS) features, but require accurate closures to remain stable and faithful; without them, solutions can drift, lose energy at the wrong rate, or develop spurious coastal artifacts. Classical analytical closures based on the eddy-viscosity hypothesis, such as the Smagorinsky and Leith models and their dynamic variants, were developed primarily for three-dimensional homogeneous turbulence. A recent benchmarking study has shown that they logically only weakly capture the SGS forcing in two-dimensional vorticity flows in the presence of coastal boundaries and interior landforms, motivating the development of data-driven closures. Among such approaches, neural-network closures have shown promise but typically return only a deterministic point estimate of the SGS term, while the mapping from resolved to unresolved scales is fundamentally non-invertible and the closure is therefore intrinsically stochastic. This non-uniqueness becomes especially pronounced in nonstationary flows, where the wake statistics themselves drift in time and a single deterministic correction can likely not represent the spread of admissible SGS responses.<\/p>\n\n\n\n
In this work, we develop and evaluate sparse and deep Gaussian process (GP) closures for under-resolved, non-stationary two-dimensional classical and \u03b2-plane vorticity flows past idealized obstacles, where non-stationarity is driven by a time modulated inflow velocity U<\/var>\u221e<\/sub>(t<\/var>) that produces a continuously evolving wake, with shedding frequency, wake width, and subgrid-scale statistics all drifting along the trajectory.<\/p>\n","protected":false},"excerpt":{"rendered":" High-resolution simulations that fully resolve all spatiotemporal scales of geophysical and turbulent flows remain a challenge in large ocean domains. Large-eddy simulations (LES) make these computations tractable by filtering out subgrid-scale (SGS) features, but require accurate closures to remain stable and faithful; without them, solutions can drift, lose energy at the wrong rate, or develop […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[182,36,5,179],"tags":[],"class_list":["post-7330","post","type-post","status-publish","format-standard","hentry","category-learning-and-data-assimilation","category-scientific-ml-deep-learning-bayesian-adaptive-modeling","category-publications","category-proceedings-of-refereed-conferences-scientific-ml"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7330","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7330"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7330\/revisions"}],"predecessor-version":[{"id":7331,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7330\/revisions\/7331"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}