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IDS.190 Topics in Bayesian Modeling and Computation

The Statistical Finite Element Method

December 11, 2019 @ 4:00 pm - 5:00 pm

Mark Girolami, University of Cambridge

E18-304

Abstract:

The finite element method (FEM) is one of the great triumphs of modern day applied mathematics, numerical analysis and software development. Every area of the sciences and engineering has been positively impacted by the ability to model and study complex physical and natural systems described by systems of partial differential equations (PDE) via the FEM .

In parallel the recent developments in sensor, measurement, and signalling technologies enables the phenomenological study of systems as diverse as protein signalling in the cell, to turbulent combustion in jet engines, to plastic deformation in bridges.

The connection between sensor data and FEM is currently restricted to data assimilation for solving inverse problems or the calibration of PDE based models. This however places unwarranted faith in the fidelity of the underlying mathematical description of the actual system under study.
If one concedes that there is ‘missing physics’ or mis-specification between generative reality and the mathematical abstraction defining the FEM then a framework to systematically characterise and propagate this uncertainty in FEM is required.

This talk will present a formal statistical construction of the FEM which systematically blends both mathematical description with observational data and provides both small and large scale examples from 3D printed structures to working rail bridges currently operated by the United Kingdom Network Rail.

Biography:

Mark Girolami is a Computational Statistician having ten years experience as a Chartered Engineer within IBM. In March 2019 he was elected to the Sir Kirby Laing Professorship of Civil Engineering (1965) within the Department of Engineering at the University of Cambridge where he also holds the Royal Academy of Engineering Research Chair in Data Centric Engineering. Girolami takes up the Sir Kirby Laing Chair upon the retirement of Professor Lord Robert Mair. Professor Girolami is a fellow of Christ’s College Cambridge.

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**Taking IDS.190 satisfies the seminar requirement for students in MIT’s Interdisciplinary Doctoral Program in Statistics (IDPS), but formal registration is open to any graduate student who can register for MIT classes.  For more information and an up-to-date schedule, please see https://stellar.mit.edu/S/course/IDS/fa19/IDS.190/

**Meetings are open to any interested researcher.

 


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