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1500 questions
9
votes
1 answer
How to find Lyapunov exponent for coupled system
Answer gives a software for calculating conditional Lyapunov exponent (CLE) for coupled oscillators in chaos synchronization. However, it is hard to follow and there is no graphical output of the plot (and it is in C, more complex). Does anyone…
Priya M
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9
votes
1 answer
What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?
I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR:
cell refinement criteria determine a list of cells that are cut
selected cells are refined:…
tmaric
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9
votes
3 answers
How do I know if my code is being vectorized by the compiler?
As exemplified by Jed Brown's answer to Costs of lookups versus calculations, using vectorized vs non-vectorized floating point operations results in much faster code. Many modern compilers claim that they can perform automatic vectorization. How…
Matthew Emmett
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9
votes
2 answers
Why are convex problems easy to optimize?
Motivated by this top answer to the question: Why is convexity more important than quasi-convexity in optimization?, I am now hoping to understand why convex problems are easy to optimize (or at least easier than quasiconvex problems).
What are some…
Amelio Vazquez-Reina
- 502
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9
votes
2 answers
Predict runtimes for dense linear algebra
I would like to predict runtimes for dense linear algebra operations on a specific architecture using a specific library. I would like to learn a model that approximates the function
$F_{op} \;::\; $input sizes$ \rightarrow $runtime
for operations…
MRocklin
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9
votes
1 answer
Matrix Balancing Algorithm
I have been writing a control system toolbox from scratch and purely in Python3 (shameless plug : harold ). From my past research, I have always complaints about the Riccati solver care.m for reasons that are technical/irrelevant.
Hence, I've been…
percusse
- 393
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9
votes
1 answer
What is the difference between Computational Science and Data Science?
Background: My PhD was in 'Computational Science'. My dissertation was on the analysis of X-Ray Diffraction Data and analysis of thermally perturbed nuclei in the overall dynamic analysis of the molecular electron density for solid state physics.…
drjrm3
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9
votes
3 answers
Is providing approximate gradients to a gradient based optimizer useless?
Is it pointless to use gradient based optimization algorithms if you can only provide a numerical gradient? If not, why provide a numerical gradient in the first place if it is trivial to perform finite differentiation for the optimization library…
professor bigglesworth
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9
votes
1 answer
Adaptive gradient descent step size when you can't do a line search
I have an objective function $E$ dependent on a value $\phi(x, t = 1.0)$, where $\phi(x, t)$ is the solution to a PDE. I am optimizing $E$ by gradient descent on the initial condition of the PDE: $\phi(x, t = 0.0)$. That is, I update $\phi(x, t =…
NLi10Me
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9
votes
4 answers
Small, unpredictable results in runs of a deterministic model
I have a sizable model (~5000 lines) written in C. It is a serial program, with no random number generation anywhere. It makes use of the FFTW library for functions using FFT - I do not know the details of the FFTW implementation , but I assume the…
boxofchalk1
- 193
- 5
9
votes
5 answers
How can I automate the process of optimizing the design of a physical object?
I'm trying to optimize a flow distributor in a tank such that the velocity and temperature distribution across any cross-section is relatively uniform. There are many parameters I can adjust to the maximum cross-sectional uniformity, such as the…
Paul
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9
votes
5 answers
How can I derive a bound on the spurious oscillations in the numerical solution of the 1D advection equation?
Suppose I had the following periodic 1D advection problem:
$\frac{\partial u}{\partial t} + c\frac{\partial u}{\partial x} = 0$ in $\Omega=[0,1]$
$u(0,t)=u(1,t)$
$u(x,0)=g(x)$
where $g(x)$ has a jump discontinuity at $x^*\in (0,1)$.
It is my…
Paul
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9
votes
2 answers
What is the worst case complexity of Conjugate Gradient?
Let $A\in \mathbb{R}^{n\times n}$, symmetric and positive definite. Suppose it takes $m$ units of work to multiply a vector by $A$. It is well known that performing the CG algorithm on $A$ with condition number $\kappa$ requires $\mathcal{O}…
fred
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9
votes
2 answers
What does the Von Neumann's stability analysis tell us about non-linear finite difference equations?
I am reading a paper [1] where they solve the following non-linear equation
\begin{equation}
u_t + u_x + uu_x - u_{xxt} = 0
\end{equation}
using finite difference methods. They also analyse the stability of the schemes using the Von Neumann's…
Hunter
- 265
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9
votes
2 answers
Markov (Chain) image generators?
Markov Chains can be used to generate, or auto-complete, text.
https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators
Training text is read, and some information about the text is remembered, for example:
The word "I" is usually followed…
alan2here
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