SteadyStateLinearPDE#

class cuqi.pde.SteadyStateLinearPDE(PDE_form, observation_map=None, **kwargs)[source]#

Linear steady state PDE.

Parameters:

  • PDE_form (callable function) – Callable function with signature PDE_form(parameter1, parameter2, …) where parameter1, parameter2, etc. are the Bayesian unknown parameters (the user can choose any names for these parameters, e.g. a, b, etc.). The function returns a tuple with the discretized differential operator A and right-hand-side b. The types of A and b are determined by what the method linalg_solve() accepts as first and second parameters, respectively.

  • observation_map (a function handle) – A function that takes the PDE solution, interpolated on grid_obs, as input and returns the observed solution. e.g. observation_map=lambda u, grid_obs: u**2.

  • kwargs – See LinearPDE for the remaining keyword arguments.

Example

See demo demos/demo24_fwd_poisson.py for an illustration on how to use SteadyStateLinearPDE with varying solver choices. And demos demos/demo25_fwd_poisson_2D.py and demos/demo26_fwd_poisson_mixedBC.py for examples with mixed (Dirichlet and Neumann) boundary conditions problems. demos/demo25_fwd_poisson_2D.py also illustrates how to observe on a specific boundary, for example.

__init__(PDE_form, observation_map=None, **kwargs)[source]#

Methods

__init__(PDE_form[, observation_map])

assemble(*args, **kwargs)

Assembles differential operator and rhs according to PDE_form

interpolate_on_observed_domain(solution)

Interpolate solution on observed space grid.

observe(solution)

Apply observation operator to the solution.

solve()

Solve the PDE and returns the solution and an information variable info which is a tuple of all variables returned by the function linalg_solve after the solution.

Attributes

grid_obs

grid_sol

grids_equal