Integrating physical and statistical models: a Bayesian approach to predictive uncertainty quantification of solitons

Dr Edward Cripps1, Mr Andrew  Manderson1, Dr  Matt Rayson5, Professor Mark Girolami2,4, Dr John Paul Gosling3, Professor Melinda Hodkiewicz6, Prof. Greg Ivey5, Dr Nicole Jones5

1Department of Mathematics and Statistics, University Of Western Australia, Perth, Australia, 2Alan Turing Institute, The British Library, London, UK, 3School of Mathematics and Statistics, University of Leeds, Leeds, UK, 4Department of Mathematics, Imperial College London, , UK, 5Oceans Graduate School, University of Western Australia, Perth, Australia, 6Faculty of Engineering and Mathematical Sciences, University of Western Australia, Perth, Australia

In shelf seas of 50 to 500 m depth solitons (non-linear internal waves), generated by tidal forcing over topography, are the main driver of extreme currents, induce some of the largest stresses on offshore infrastructure, drive sediment resuspension, and influence dynamic positioning systems during operations. This work demonstrates how recent advances in Bayesian statistical methods and computing integrates with physical models to predict solitons, provide industrial tools for decision making under uncertainty and refine our scientific understanding of associated ocean dynamic processes.  Using data collected on the North West Shelf, we estimate a Bayesian hierarchical model of density stratification and initial amplitude inputs and propagate the results through the Kortweg-de Vries (KdV) equation soliton forecast model.  Posterior distributions summarise the predictive uncertainty of maximum soliton amplitudes, density stratification characteristics, isopycnal heights and various ocean dynamic processes.  Code is implemented in the probabilistic programming language Stan to estimate the Bayesian model and prototype frontend software has been developed.    The work is multidisciplinary and is a collaboration between The Industrial Transformation Hub for Offshore Floating Facilities, University of Western Australia, and The Programme for Data Centric Engineering, Alan Turing Institute-Lloyd’s Register Foundation, London.


Edward Cripps is a researcher at the Department of Mathematics and Statistics, University of Western Australia, in Bayesian statistical methods, with a particular interest in spatio-temporal oceanic and atmospheric applications.   He is Chief Investigator for the Data Analytics programme of the ARC Industrial Transformation Research Hub for Offshore Floating Facilities and the ARC Industrial Transformational Training Centre for Transforming Maintenance through Data Science.

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