Abstract: The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. Here, we present a unifying framework for blending mechanistic and machine-learning approaches for identifying dynamical systems from data. This framework is agnostic to the chosen machine learning model parameterization, and casts the problem in both continuous- and discrete-time. We will also show recent developments that allow these methods to learn from noisy, partial observations. We first study model error from the learning theory perspective, defining the excess risk and generalization error. For a linear model of the error used to learn about ergodic dynamical systems, both excess risk and generalization error are bounded by terms that diminish with the square-root of T (the length of the training trajectory data). In our numerical examples, we first study an idealized, fully-observed Lorenz system with model error, and demonstrate that hybrid methods substantially outperform solely data-driven and solely mechanistic-approaches. Then, we present recent results for modeling partially observed Lorenz dynamics that leverages both data assimilation and neural differential equations.

Biography: Matthew Levine is a graduate student in computing and mathematical sciences at Caltech. His work focuses on improving the prediction and inference of physical systems by blending machine learning, mechanistic modeling, and data assimilation techniques. He aims to build robust, unifying theory for these approaches, as well as develop concrete applications. He has worked substantially in the biomedical sciences, and enjoy collaborating on impactful applied projects.

Abstract: The ocean is dominated by kinematic features, such as gyres, fronts, and mesoscale eddies, that persist for much longer than typical dynamical timescales. Due to their capacity to transport heat, salt, carbon, and other biogeochemical tracers over long distances, these coherent structures play an important role in climate, biology, and small-scale mixing. However, because of their Lagrangian (or flow-following) nature, identifying and tracking these features, and ultimately quantifying their contribution to transport processes, is challenging. In this talk, I will examine transport and mixing in the ocean by coherent structures through the framework of finite-time coherent sets. Coherent sets describe regions of phase space that minimise mixing along their boundaries over a finite time window. They identify barriers to transport and provide the skeleton around which more complex or turbulent dynamics occurs. I will present the results of three applications of the framework to: (i) study the persistence and material coherence of an Agulhas ring; (ii) extend the framework to domains containing multiple ocean eddies; and (iii) investigate and quantify cross-front transport in the Southern Ocean.

Biography: Michael Denes is a Ph.D. student in the School of Mathematics and Statistics at the University of New South Wales, supervised by Professor Gary Froyland and Dr Shane Keating. He holds a BSc. (Honours 1) in Applied Mathematics and Computer Science from the University of Sydney. His current research interests include mathematical oceanography, geophysical fluid dynamics, and dynamical systems.

Abstract: This talk will address some of the latest developments in marine robotics and how they are being adapted to address new challenges from different communities. Science communities in general want more data (longer space and time series), to measure more parameters, to increase sampling frequencies, and to ensure data quality. They also want to automate processes, from data gathering to processing and communicating, so that these data can be available sooner, and with less risk for operators. Industry also looks for robotic tools to automate processes, replacing operators for better efficiency and safety, reducing logistics and maintenance costs. One of the goals of the robotics community has been to obtain more data about the oceans by extending capabilities in space and time ranges and resolutions. A significant part of this effort has been enabled by a series of autonomous robotic platforms, and many of them are already available off-the-shelf to non-specialist users. However, some of the more demanding challenges cannot be correctly address by these now-ubiquitous solutions and require specific improvements. The Center for Robotics and Autonomous System of INESC TEC in Porto, Portugal, has been involved in many R&D projects developing cutting-edge technology for the sea. The Center aggregates specialists in several competencies associated with autonomous marine robotics, therefore it has participated in multiple international R&D projects to ensure the development of critical subsystems. In some cases, the Center has led the development of complete integrated solutions, assembling a combination of these custom subsystems with others developed by R&D partners. The talk will describe some of these subsystems, together with examples of past and current projects where they are being implemented.

Biography: Nuno Cruz holds a MSc. in Digital Systems Engineering from UMIST, UK, and a PhD. in Electrical Engineering from the University of Porto, in Portugal. He is currently an Assistant Professor at the Faculty of Engineering of the University of Porto and a Coordinator at the Centre for Robotics and Autonomous Systems at INESC TEC. Nuno Cruz is an Associate Editor of the IEEE Journal of Oceanic Engineering and has over 100 publications in journals and proceedings of international conferences. He has been involved in the development and deployment of marine robotic vehicles for more than 20 years. He has led the design of multiple autonomous vehicles at the University of Porto and INESC TEC, namely the Zarco and Gama ASVs and the MARES and TriMARES AUVs. His current research interests include the development of strategies for the efficient use of autonomous vehicles at sea, including the concept of adaptive sampling.