CUQIpy-FEniCS 0.4.0.post0.dev45

CUQIpy plugin for FEniCS

CUQIpy-FEniCS

CUQIpy-FEniCS is a plugin for CUQIpy software package. It provides an interface between FEniCS PDE models and CUQIpy modules.

Installation

First install FEniCS (we recommend using Anaconda from the available installation options). Then install CUQIpy-FEniCS with pip:

pip install cuqipy-fenics

If CUQIpy is not installed, it will be installed automatically.

Quickstart

import numpy as np
import matplotlib.pyplot as plt
import cuqi
import cuqipy_fenics

# Load a fenics forward model and data from testproblem library
model, y_data, info = cuqipy_fenics.testproblem.FEniCSDiffusion1D.get_components(
    dim=20,
    endpoint=1,
    exactSolution='smooth_step',
    mapping='exponential',
    SNR=10000,
    left_bc=0,
    right_bc=8
)

# Set up Bayesian model
x = cuqi.distribution.GMRF(np.zeros(model.domain_dim),
                           25, 1, 'zero', geometry=model.domain_geometry)
# y ~ N(model(x), 0.01^2)
y = cuqi.distribution.Gaussian(mean=model(x), cov=0.05**2)

# Set up Bayesian Problem object
BP = cuqi.problem.BayesianProblem(y, x).set_data(y=y_data)

# Sample from the posterior
samples = BP.sample_posterior(5000)

# Analyze the samples
samples.burnthin(1000).plot_ci(95, plot_par=True,
                               exact=info.exactSolution, linestyle='-', marker='.')

For more examples, see the demos folder.