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The effectiveness of the approach is demonstrated through the solution of parameter estimation problems with over 4100 ordinary differential equations, 16,000 algebraic equations and 2100 degrees of freedom in a distributed cluster.
Finally, it is important to acknowledge that, because our model represents the elementary interactions underlying coupling, it is too underdetermined to identify a single "correct" solution of parameter values that may be expected to represent the "real" solution.
It has been largely recognized that solving the solution of parameter identification problems becomes harder with the size of the problem, particularly when the ratio between the number of observables and experimental data and the number of parameters is low, since these induce multimodality and lack of structural and/or practical identifiability.
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Although there will not be any issue for parameter sensitivity in our system because of linear events, multiple solutions of parameter space, Js, can occur [13].
Here it is important to make use of the previously converged solutions of parameters (coefficients) for the next initial parameters of such large dimensions.
Figure 1f shows a 2D parameter projection of the generated parameter ensemble, in which each blue dot represents a parameter combination in the ensemble and the largest dot corresponds to the optimal solution of the parameter estimation step.
We are presenting a new solution of plasma parameter determination suitable for small and fast solar wind monitors.
Three different optimization algorithms for the solution of the parameter estimation problem are compared from within the EFCOSS environment.
The maximum likelihood solution of unknown parameter α is regarded as the estimated value, and then, we sample the bimodal PDF p(x).
In particular, a great improvement is shown in case of a unique reduction matrix whose columns span the solution of the parameter space of interest in an accurate enough way, and in case of substructuring reduction techniques.
A well-known approach for shape optimization problems, which is called the discrete approach, describes a domain shape with parameters of finite numbers and finds out an optimum solution of the parameters by utilizing mathematical programing methods.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com