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Sparse Regression and Adaptive Feature Generation for the Discovery of Dynamical Systems

Kulkarni, C.S., A. Gupta, and P.F.J. Lermusiaux, 2020. Sparse Regression and Adaptive Feature Generation for the Discovery of Dynamical Systems. In: InfoSymbiotics/DDDAS2020 Boston, 2-4 October 2020. In press.

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first examine the generic methodology of learning interpretable equation forms from data, proposed by Brunton et al. [2016], followed by performance of LASSO for this purpose. We then develop a new algorithm that uses the dual of LASSO optimization for higher accuracy and stability. We then obtain a novel algorithm that learns the candidate function library in a completely data-driven manner to distill the governing equations of the dynamical system. This is achieved via sequentially thresholded ridge regression (STRidge) over a orthogonal polynomial space. The performance of the methods is illustrated using the Lorenz 63 system, the quadratic Lorenz system, and a marine ecosystem model.

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Fish Modeling and Bayesian Learning for the Lakshadweep Islands

Gupta, A., P.J. Haley, D.N. Subramani, and P.F.J. Lermusiaux, 2019. Fish Modeling and Bayesian Learning for the Lakshadweep Islands. In: OCEANS '19 MTS/IEEE Seattle, 27-31 October 2019, doi: 10.23919/OCEANS40490.2019.8962892

In fish modeling, a significant amount of uncertainty exists in the parameter values, parameterizations, functional form of model equations, and even the state variables themselves. This is due to the complexity and lack of understanding of the processes involved, as well as the measurement sparsity. These challenges motivate the present proof-of-concept study to simultaneously learn and estimate the state variables, parameters, and model equations from sparse observations. We employ a novel dynamics-based Bayesian learning framework for high-dimensional, coupled fish-biogeochemical-physical partial-differential equations (PDEs) models, allowing the simultaneous inference of the augmented state variables and parameters. After reviewing the status of ecosystem modeling in the coastal oceans, we first complete a series of PDE-based learning experiments that showcase capabilities for fish-biogeochemical-physical model equations and parameters, using nonhydrostatic Boussinesq flows past a seamount. We then showcase realistic ocean primitive-equation simulations and analyses, using fish catch data  for the Lakshadweep islands in India. These modeling and learning efforts could improve fisheries management from a standpoint of sustainability and efficiency.

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Data-driven Learning and Modeling of AUV Operational Characteristics for Optimal Path Planning

Edwards, J., J. Smith, A. Girard, D. Wickman, P.F.J. Lermusiaux, D.N. Subramani, P.J. Haley, Jr., C. Mirabito, C.S. Kulkarni, and, S. Jana, 2017. Data-driven Learning and Modeling of AUV Operational Characteristics for Optimal Path Planning. In: Oceans '17 MTS/IEEE Aberdeen, 1-5, 19-22 June 2017, DOI: 10.1109/OCEANSE.2017.8084779

Autonomous underwater vehicles (AUVs) are used to execute an increasingly challenging set of missions in commercial, environmental and defense industries. The resources available to the AUV in service of these missions are typically a limited power supply and onboard sensing of its local environment. Optimal path planning is needed to maximize the chances that these AUVs will successfully complete long endurance missions within their power budget. A time-optimal path planner has been recently developed to minimize AUV mission time required to traverse a dynamic ocean environment at a specified speed through the water. For many missions, time minimization is appropriate because the AUVs operate at a fixed propeller speed. However, the ultimate limiting constraint on AUV operations is often the onboard power supply, rather than mission time. While an empirical or theoretical relationship between mission time and power could be applied to estimate power usage in the path planner, the real power usage and availability on an AUV varies mission-to-mission, as a result of multiple factors, including vehicle buoyancy, battery charge cycle, fin configuration, and water type or quality. In this work, we use data collected from two mid-size AUVs operating in various conditions to learn the mission-to-mission variability in the power budget so that it could be incorporated into the mission planner.
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