FEniCSDiffusion1D

class cuqipy_fenics.testproblem.FEniCSDiffusion1D(dim=100, endpoint=1, exactSolution=None, SNR=100, observation_operator=None, mapping=None, left_bc=0, right_bc=1)

1D Diffusion PDE problem using FEniCS. The problem has Dirichlet boundary conditions.

Parameters:

• dim (int, Default 100) – Dimension of the 1D problem

• endpoint (float, Default 1) – Endpoint of the 1D grid (starts at 0).

• exactSolution (ndarray, CUQIarray, Default None) – Exact solution used to generate data. If None a default exact solution is chosen.

• SNR (float, Default 100) – Signal-to-noise ratio.

• mapping (str or callable) – mapping to parametrize the Bayesian parameters. If provided as string, it can take one of the values: [‘exponential’]

data

Generated (noisy) data

Type:

ndarray

model

The forward model

Type:

cuqi.model.Model

prior

Distribution of the prior (Default = None)

Type:

cuqi.distribution.Distribution

likelihood

Likelihood function.

Type:

cuqi.likelihood.Likelihood

exactSolution

Exact solution (ground truth)

Type:

ndarray

exactData

Noise free data

Type:

ndarray

infoSring

String with information about the problem, noise etc.

Type:

str

MAP()

Compute MAP estimate of posterior. NB: Requires prior to be defined.

sample_posterior(Ns)

Sample Ns samples of the posterior. NB: Requires prior to be defined.

__init__(dim=100, endpoint=1, exactSolution=None, SNR=100, observation_operator=None, mapping=None, left_bc=0, right_bc=1)

Methods

MAP([disp, x0])	Compute the Maximum A Posteriori (MAP) estimate of the posterior.
ML([disp, x0])	Compute the Maximum Likelihood (ML) estimate of the posterior.
UQ([Ns, Nb, percent, exact, experimental])	Run an Uncertainty Quantification (UQ) analysis on the Bayesian problem and provide a summary of the results.
__init__([dim, endpoint, exactSolution, ...])
get_components()	Method that returns the model, the data and additional information to be used in formulating the Bayesian problem.
sample_posterior(Ns[, Nb, callback, ...])	Sample the posterior.
sample_prior(Ns[, callback])	Sample the prior distribution.
set_data(**kwargs)	Set the data of the problem.

Attributes

data	Extract the observed data from likelihood
likelihood	The likelihood function.
model	Extract the cuqi model from likelihood.
posterior	Create posterior distribution from likelihood and prior.
prior	The prior distribution