# Questions tagged [inverse-problem]

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

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### Identifying an unknown P.D.E. from solution data

I have a black-box simulation that produces the time evolution of a probability density function p(x, t) in 1 dimension from arbitrary initial conditions p(x, 0). The underlying simulation occurs on a ...
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### Invert a huge sparse operator;

please help me with this question, I want to invert a huge sparse (non-circulant) this below in a $Ax=y$ equation: $$(\lambda I+ \beta D+ \sigma C)x=y$$ where I is an Identity Matrix,D is a Diagonal ...
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### Compute point-spread-function between original and blurred image

Take an image $f$ with some characters on it (below, hjFu3). Let's apply a filter $h$ on it to obtain a second image $g$ where the text is not visible. Is there a way to compute what kind of filter $h$...
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### Inverse problem with uncertain forward operator

Suppose I want to solve a linear inverse problem. In this example we take a convolution with the kernel: $$\frac{1}{(y^2+z^2)^{3/2}}$$ We only take a fixed $z$ for the computation and convolve with ...
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### Inverse advection-diffusion problem, solving for a drift coefficient with experimental data?

I am investigating a physical process where I believe the 1-D advection-diffusion equation: \frac{\partial u}{\partial t} = -\frac{\partial}{\partial x}[\mu(x,t) u(x,t)] + \frac{\...
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### Do you spend time reading pure math books as a graduate student on computational math

I am going to start my first year of a research-oriented master program on inverse problem. From what I know, unlike pure math students, applied math students usually don't spend the first year ...
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### How can I determine the initial values of pseudo-random number generator if the sequence is given?

Suppose I knew that a random number sequence was generated by a linear congruential generator. That is, $x_{n+1}=(aX_n+c) \bmod m$ If I am given the entire period (or at least a large contiguous ...
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### Smoothness regularisation of a 2D field on a triangular mesh?

I'm working on an inverse problem where the solution is the values of a 2D scalar field at the vertices of a 2D triangular mesh, such that the field can be defined continuously inside the mesh via ...
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### numerical solution of an under-determined linear equation in high dimensions

I need to solve a linear regression problem $$Ax=y$$ which is hugely underdetermined. I have around $10^6$ features but only $10^3$ equations. So $A$ is a $1,000\times 1,000,000$ matrix and $y$ a ...
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### Numerical error of a spectral-domain Poisson solver

In $\mathbb{R}^n$, I would like to solve a Poisson equation (given $f$, solve for $u$): $$\nabla^2 u = f$$ assuming Neumann boundary condition (i.e. $\partial u = 0$ at boundaries). I solved it in ...
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### Edge and Nodal finite element methods in MATLAB for Magnetic induction tomography

What is the difference between edge finite elements and nodal finite elements? This for use in modeling the eddy current problem in classical electromagnetism. I am attempting to convert MATLAB code ...
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### Algorithm for optimizing Ax = b with unknown A and known x values

I would like to solve for the optimum $A$ values for a series of matrix equations $Ax_{1} = b_{1}, Ax_{2} = b_{2} ... Ax_{n} = b_{n}$ where only the $x$ values are known and when I start with an ...
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### Computing inverse functions of functions of two variables

There are several functions of two or three variables that I am working with. For this question I have made a small set showing the resistivity, $\rho$, in n$\Omega$m, of copper as a function of its ...
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### reformulating inverse problem as multi-objective optimization

I'm working on an inverse problem for my Ph.D. research, for which I'll write the objective functional as $J(\theta) = E(G(\theta) - u^o)$, where $\theta$ are the parameters, $G$ is the forward map ...
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### Recommended Route for Mastering Inverse PDE Problems

I would like to master Inverse PDE Problems particularly with the use of Finite Elements. My problem is I don't know where to start. Should I begin by reading a book on Inverse Problems or on PDE-...
Well, in a numerical technique test we were given the following problem: A physical phenomenon is modeled such that, $F(f,d) = A(f)/d^2 + L$; Where, $F$ is a function of frequency $f$ and distance \$...