Our generalized neural closure models (gnCMs) based on unified neural partial differential equations (PDEs) are applied to ocean, sea ice, and chaotic systems. We augment existing/low-fidelity dynamical models directly in their PDE forms with both Markovian and non-Markovian neural network (NN) closures. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible gnCMs provide full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We apply the gnCMs to learning experiments with advecting nonlinear waves, shocks, ocean acidification, ocean submesoscales, and sea ice models. We highlight applications to chaotic systems, emphasizing the need for adaptive learning schemes. Our learned gnCMs discover missing chaotic physics, find leading numerical error terms, discriminate among candidate functional forms in an interpretable fashion, achieve generalization, and compensate for the lack of complexity in simpler models.

Abstract: The New England Seamount Chain in the North Atlantic presents a combination of complex bathymetry and highly dynamic currents due to their location near the Gulf Stream. The Task Force Ocean Biological Soundscapes team have sampled simultaneous ambient noise, biological oceanography, and bio-physical oceanographic sections around the Kelvin Seamount to better understand the impacts of both the seamount bathymetry and Gulf Stream features on the structure of pelagic biology in the water column and physical oceanographic properties. During an October 2023 field campaign on the R/V Langseth, Tropical Storm Phillippe interrupted a research cruise such that oceanographic sections were collected before and after the storm, and water column as well as bottom mounted ambient noise data were recorded before, during, and after the storm. While the storm and periodic ship traffic affect ambient noise levels as historically described by Piggott and Wenz, oceanographic mixing and bio-physical interactions are more complex with Gulf Stream front and eddy dynamics appearing to be more significant drivers than potential mixing associated with the tropical storm passage.

Abstract: The mass loss from the Greenland and Antarctic ice sheets is a major contribution to global sea level rise. To generate accurate projections of ice sheet mass loss, it’s crucial to model the dynamics and evolution of ice sheets, while also considering the uncertainties present in observational data and computational models. In this presentation, we discuss state-of-the-art methods for calibrating Greenland and Antarctic ice sheet models by inverting for high-dimensional model parameters. This involves the use of large-scale PDE (Partial Differential Equation)-constrained optimization techniques and the application of Bayesian inference to efficiently approximate the posterior distribution of the parameters we infer. We then turn our attention to the Humboldt glacier in Greenland and model how uncertainties in the basal friction parameter influence the glacier’s mass loss. We present recent work employing multi-fidelity methods to reduce the computational cost of estimating the mean and variance of glacier mass-change. Our results show that the multi-fidelity approach leads to over an order of magnitude speed-up compared to the traditional Monte Carlo method for uncertainty propagation.

Biography: Dr. Mauro Perego is a computational scientist at the Center for Computing Research, Sandia National Laboratories. Mauro achieved his PhD in mathematical engineering at the Polytechnic University of Milan, Italy. His work spans several aspects of scientific computing, including the discretization and solution of nonlinear partial differential equations, numerical optimization, uncertainty quantification, and scientific machine learning. His current research is in large part applied to ice sheet modeling, with the ultimate goal of providing reliable projections of sea-level rise.

Congratulations to Wael, Aaron, and Pierre for co-authoring a paper entitled “A Wide-Area Deep Ocean Floor Mapping System: Design and Sea Tests,” which appeared in Geomatics in 2023. The full paper is available from our publications website.

Read more about this award and previous MIT Lincoln Laboratories Best Paper & Best Invention Awards.