Exploring Model Misspecification in Statistical Finite Elements via Shallow Water Equations

by   Connor Duffin, et al.

The abundance of observed data in recent years has increased the number of statistical augmentations to complex models across science and engineering. By augmentation we mean coherent statistical methods that incorporate measurements upon arrival and adjust the model accordingly. However, in this research area methodological developments tend to be central, with important assessments of model fidelity often taking second place. Recently, the statistical finite element method (statFEM) has been posited as a potential solution to the problem of model misspecification when the data are believed to be generated from an underlying partial differential equation system. Bayes nonlinear filtering permits data driven finite element discretised solutions that are updated to give a posterior distribution which quantifies the uncertainty over model solutions. The statFEM has shown great promise in systems subject to mild misspecification but its ability to handle scenarios of severe model misspecification has not yet been presented. In this paper we fill this gap, studying statFEM in the context of shallow water equations chosen for their oceanographic relevance. By deliberately misspecifying the governing equations, via linearisation, viscosity, and bathymetry, we systematically analyse misspecification through studying how the resultant approximate posterior distribution is affected, under additional regimes of decreasing spatiotemporal observational frequency. Results show that statFEM performs well with reasonable accuracy, as measured by theoretically sound proper scoring rules.


page 9

page 11


Statistical Finite Elements via Langevin Dynamics

The recent statistical finite element method (statFEM) provides a cohere...

Low-rank statistical finite elements for scalable model-data synthesis

Statistical learning additions to physically derived mathematical models...

The Statistical Finite Element Method

The finite element method (FEM) is one of the great triumphs of modern d...

A balanced finite-element method for an axisymmetrically loaded thin shell

We analyse a finite-element discretisation of a differential equation de...

A Bayesian Approach to Modeling Finite Element Discretization Error

In recent years, there has been a surge of interest in the development o...

Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction

We present an energy conserving space discretisation based on a Poisson ...

Inferring Displacement Fields from Sparse Measurements Using the Statistical Finite Element Method

A well-established approach for inferring full displacement and stress f...

Please sign up or login with your details

Forgot password? Click here to reset