MUQ Example

Just a small example, playing around with MUQ. We try to find some parameters of an ODE model.

ODE Model

We solve the ODE problem $u^{\prime\prime} = - \omega^2 u$ with initial conditions $u(0) = \alpha$, $u^\prime(0) = 0$ The true solution is $u(t) = \alpha \cos(\omega t)$.

The goal is to invert for parameters $\alpha, \omega$.

Structure of the repository

• analysis: plot script for the 2d density
• doctest: external include for doctest
• src/MPI: Some wrappers for MPI functionality
• src/ODEModel: Simple implicit Euler solver for the ODE problem above
• src/UQ: Everyting for uncertainty quantification
• src/generate_true_solution.py: generates the function $u$ with some fixed parameters $\alpha, \omega$
• src/main.cpp: main script, which starts the UQ runner.
• tests: Contains unit tests, probably not working

How to run

• mkdir build && cd build Note: I use muq2 with commit 7fafda2.
• cmake ..
• make -j 8
• python ../src/generate_true_solution.py
• mpirun ./main
• python ../analyis/plot_density.py samples.h5