How to solve the stochastic partial differential equation that gives a Matérn random field using the finite element method

03/10/2018
by   Haakon Bakka, et al.
0

This tutorial teaches parts of the finite element method (FEM), and solves a stochastic partial differential equation (SPDE). The contents herein are considered "known" in the numerics literature, but for statisticians it is very difficult to find a resource for learning these ideas in a timely manner (without doing a year's worth of courses in numerics). The goal of this tutorial is to be pedagogical and explain the computations/theory to a statistician. This is not a practical tutorial, there is little computer code, and no data analysis.

READ FULL TEXT
research
08/28/2020

Convergence of adaptive stochastic collocation with finite elements

We consider an elliptic partial differential equation with a random diff...
research
10/12/2017

A Finite Element Computational Framework for Active Contours on Graphs

In this paper we present a new framework for the solution of active cont...
research
10/05/2021

Deep Learning for the Approximation of a Shape Functional

Artificial Neuronal Networks are models widely used for many scientific ...
research
11/05/2021

MetaFEM: A Generic FEM Solver By Meta-expressions

Current multi-physics Finite Element Method (FEM) solvers are complex sy...
research
03/16/2022

Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks

We propose a new method for spatio-temporal forecasting on arbitrarily d...
research
09/06/2021

Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy

The stochastic partial differential equation approach to Gaussian proces...
research
12/27/2022

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