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CUQI-DTU / CUQIpy

https://cuqi-dtu.github.io/CUQIpy/
Apache License 2.0
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Support inference of multiple unknown parameters (feature request) #351

Open PeterARBork opened 10 months ago

PeterARBork commented 10 months ago

In solving the inverse problem for a 1D advection-diffusion problem where I have tracer concentrations but want both a constant advection parameter and a spatially varying diffusion parameters, I need to infer these two different types of unknown parameters.

For example we could infer both parameter c and a by specifying the PDE form in the following fashion:

## PDE form (constant diffusion coefficient case)
def PDE_form_const(c, a, tau_current):
    return (D_c_const(c, a), g_const(c, a, tau_current), initial_condition)

## CUQIpy PDE object (constant diffusion coefficient case)
PDE_const = TimeDependentLinearPDE(PDE_form_const, tau, grid_sol=grid,
                             method='backward_euler', 
                             grid_obs=locations,
                            time_obs=times)

Where we can give c and a their own priors (for example a normal for a and a random field for c).

amal-ghamdi commented 10 months ago

Many thanks @PeterARBork for raising this issue! We are looking into it 😊👍