It was good…

Low-propulsion vessels can take advantage of powerful ocean currents to navigate towards a destination. Recent results demonstrated that vessels can reach their destination with high probability despite forecast errors. However, these results do not consider the critical aspect of safety of such vessels: because their propulsion is much smaller than the magnitude of surrounding currents, they might end up in currents that inevitably push them into unsafe areas such as shallow waters, garbage patches, and shipping lanes. In this work, we first investigate the risk of stranding for passively floating vessels in the Northeast Pacific. We find that at least 5.04% would strand within 90 days. Next, we encode the unsafe sets as hard constraints into Hamilton-Jacobi Multi-Time Reachability to synthesize a feedback policy that is equivalent to re-planning at each time step at low computational cost. While applying this policy guarantees safe operation when the currents are known, in realistic situations only imperfect forecasts are available. Hence, we demonstrate the safety of our approach empirically with large-scale realistic simulations of a vessel navigating in high-risk regions in the Northeast Pacific. We find that applying our policy closed-loop with daily re-planning as new forecasts become available reduces stranding below 1% despite forecast errors often exceeding the maximal propulsion. Our method significantly improves safety over the baselines and still achieves a timely arrival of the vessel at the destination.

Abstract: Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a judicious usage in modelling fluid evolution, one needs to calibrate the amplitude of the noise to data. In this paper we address this requirement for the stochastic rotating shallow water (SRSW) model. This work is a continuation of [1], where a data assimilation methodology has been introduced for the SRSW model. The noise used in [1] was introduced as an arbitrary random phase shift in the Fourier space. This is not necessarily consistent with the uncertainty induced by a model reduction procedure. In this paper, we introduce a new method of noise calibration of the SRSW model which is compatible with the model reduction technique. The method is generic and can be applied to arbitrary stochastic parametrizations. It is also agnostic as to the source of data (real or synthetic). It is based on a principal component analysis technique to generate the eigenvectors and the eigenvalues of the covariance matrix of the stochastic parametrization. For SRSW model covered in this paper, we calibrate the noise by using the elevation variable of the model, as this is an observable easily obtainable in practical application, and use synthetic data as input for the calibration procedure. This is joint work with Alexander Lobbe, Oana Lang, Peter Jan van Leeuwen, and Roland Potthast.

[1] Lang, O., P.J. van Leeuwen, D. Crisan, and R. Potthast, 2022. Bayesian Inference for Fluid Dynamics: A Case Study for the Stochastic Rotating Shallow Water Model. Frontiers in Applied Mathematics and Statistics 8. doi:10.3389/fams.2022.949354

Biography: Dan Crisan is a Professor of Mathematics at the Department of Mathematics of Imperial College London and Director of the EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth. His long-term research interests lie broadly in Stochastic Analysis, a branch of Mathematics that looks at understanding and modelling systems that behave randomly. He is one of the four PIs of the project Stochastic Transport in Upper Ocean Dynamics. This project has received a six-year Synergy ERC award.

https://www.abc6.com/high-surf-from-hurricane-teddy-attracts-surfers-from-across-region/

Abstract: Understanding and predicting the Earth system have profound impacts on both society and environments. Despite its importance, Earth system prediction presents significant challenges. The current observing system captures only a fragment of the Earth’s complexity, necessitating reliance on Earth system models to bridge the gaps in space, time, and spectral regions not covered by observations. Over time, these models have evolved remarkably—from empirical, to theoretical, to computational, and now are moving to data-driven machine learning (ML) approaches. In this seminar, we will explore a range of ML methodologies to enhance Earth system predictability. The topics include surrogate modeling, inversion-free prediction, and invertible neural networks to reduce computational costs of numerical Earth system model simulation and uncertainty quantification, and physics-informed, explainable, and trustworthy ML techniques to advance data-driven Earth system predictions. The applications of these methods cover terrestrial ecosystem model, hydrological model, and geological carbon storage.

Biography: Dr. Dan Lu is a Senior Staff Scientist in Computational Earth Sciences Group at Oak Ridge National Laboratory (ORNL). She earned her Ph.D. in Computational Hydrology at Florida State University in 2012, and joined ORNL in 2013 after one-year postdoctoral appointment at the U. S. Geological Survey. Her research interest includes machine learning, uncertainty quantification, surrogate modeling, inverse modeling, sensitivity analysis; experimental design, and numerical simulations in earth, climate, and environment sciences. She is leading several ML related projects funded by different programs across U.S. Department of Energy. She is currently serving as an Associate Editor of the journal Artificial Intelligence for the Earth Systems, an Associate Editor of the journal Frontiers in Water, and a Topic Editor of the journal Geoscientific Model Development.