Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [inverse-problem]

For questions pertaining to methods to estimate input parameters based upon output data.

Traditionally, we set the parameters of a model first (e.g. a partial differential equation), then observe the behavior of the system. An "inverse problem" is doing the reverse. We start with the observations of the output of the system, and try to determine the parameters of the model that produce these observations. Inverse theory describes different methods for accomplishing this task.

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pointwise vs. continuous observations in PDE inverse problem

I work on an inverse problem for my Ph.D. research, which for simplicity's sake we'll say is determining $\beta$ in $L(\beta)u \equiv -\nabla\cdot(k_0e^\beta\nabla u) = f$ from some observations $u^o$; $k_0$ is a constant and $f$ is known. This is…
Daniel Shapero
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Finding the fixed point of an operator

What numerical methods are available for finding the fixed point of an operator $A$ that is acting on functions $f : [a,b] \rightarrow [a,b]$? I am looking for the function $f$ for which $Af = f$. Essential details: My function $f$ is actually a…
Szabolcs
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Is there any theory of the minimum amount of data for tomographic reconstruction?

I'm doing an experiment on synthetic data and I want to generate enough data but not too much. So I wonder if there is any rule for the minimum number of projection angles and detector count. For example, in 2D parallel beam case, if the image size…
jakeoung
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Inverse problems with a discrete set of known parameters

What are the techniques on inverse problems to discover the distribution of parameters from a discrete set of values? For instance, I know that my domain where the PDE is defined is made up of materials A, B and C, but I do not know how they are…
balborian
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Inverse problem with changing number of variables

I have an inverse problem in which the optimal positions for a variable number of injections needs to be determined. If the number of injections was fixed, I could easily imagine implementing Simplex or Genetic Algorithm (or really any optimisation…
mbcx9rb9
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adjoint method for degenerate problems

For the sake of the rest of the question, I'm interested in the porous medium equation $$S\frac{\partial\phi}{\partial t} = \nabla\cdot K\phi\,\nabla\phi$$ where $S$ and $K$ are spatially-variable coefficients and $\phi$ (the hydraulic head) is the…
Daniel Shapero
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