Truncated fluid and ocean models omit subgrid physics and introduce numerical biases that degrade forecasts. We present a Bayesian, data-driven closure for 2-D finite-volume solvers that learns the dynamical discrepancy between low-resolution (LR) and high-resolution (HR) simulations. Using sparse variational Gaussian processes (GPs) and deep GPs, we map resolved features (local velocities and gradients) to a closure source term that corrects LR tendencies toward HR dynamics while quantifying predictive uncertainty. GPs can be well-suited to closure modeling in fluids because they encode smoothness\/invariance via kernels, learn nonparametric mappings from data, and return uncertainty estimates alongside the mean correction. The trained GP is embedded intrusively into a numerical finite volume framework and evaluated online each coarse time step, keeping the closure consistent with the numerics.<\/p>\n\n\n\n
We assess the approach on three test beds: (i) flow past a cylinder across multiple Reynolds numbers; (ii) tidally modulated flow past a cylinder with time-varying Reynolds number; and (iii) bottom gravity currents. Models are trained on HR downsamplings\u2013LR pairs and then tested across different regimes. We evaluate performance by using field-wise errors and wake metrics: mean velocity profiles in the near and far wake, lift C_L and drag C_D coefficients, and Strouhal number St. Relative to LR baselines without closure, GP closures reduce L2 \/ L\u221e errors of the resolved fields and bring mean velocity, C_D\/C_L, and St closer to HR references across trained Reynolds numbers. The online GP closure adds negligible wall-clock cost relative to the fluid step, preserves the conservative finite-volume structure, and provides uncertainty estimates. Overall, these results demonstrate a practical, uncertainty-aware GP closure that improves coarse-grid fidelity for 2-D fluid and ocean flows, which could potentially be extended to 3-D ocean frameworks.<\/p>\n","protected":false},"excerpt":{"rendered":"
Truncated fluid and ocean models omit subgrid physics and introduce numerical biases that degrade forecasts. We present a Bayesian, data-driven closure for 2-D finite-volume solvers that learns the dynamical discrepancy between low-resolution (LR) and high-resolution (HR) simulations. Using sparse variational Gaussian processes (GPs) and deep GPs, we map resolved features (local velocities and gradients) to […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[243],"tags":[],"class_list":["post-7219","post","type-post","status-publish","format-standard","hentry","category-presentations"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7219","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=7219"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7219\/revisions"}],"predecessor-version":[{"id":7220,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/7219\/revisions\/7220"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}