Self-consistent regularization.
The second one takes into account slit/cylindrical pores and voids between spherical particles with the self-consistent regularization (SCV/SCR) [41 44].
The nitrogen desorption data were used to compute the pore size distributions (PSD, differential f V~dV p/dR and f S~dS/dR) using a self-consistent regularization (SCR) procedure under nonnegativity condition (f V ≥ 0 at any pore radius R) at a fixed regularization parameter α = 0.01 with voids (V) between spherical nonporous nanoparticles packed in random aggregates (V/SCR model) [49].
The nitrogen desorption data were used to compute the pore size distributions (PSD, differential fV(R) ~ dVp/dR and fS R) ~ dS/dR) using a self-consistent regularization (SCR) procedure under non-negativity condition (fV(R) ≥ 0 at any pore radius R) at a fixed regularization parameter α = 0.01.
The nitrogen desorption data were used to compute the pore size distributions (differential f V ~ dV p/dR and f S ~ dS/dR) using a self-consistent regularization (SCR) procedure under non-negativity condition (f V ≥ 0 at any pore radius R) at a fixed regularization parameter α = 0.01 with voids (V) between spherical nonporous nanoparticles packed in random aggregates (V/SCR model) [27].
This means the numerical results are not so good for stronger 'smoothness' assumptions on the exact solution f ( x ) which is consistent with the Tikhonov regularization method in [27].
A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field.
While most feature selection techniques are based on heuristics, l1- l2 regularization is asymptotically consistent from the statistical viewpoint, i.e. theoretical results [ 36] guarantee that the best possible estimator is found as the number of training samples increases.
The distribution of the obtained model parameters is highly non-Gaussian, in particular shown in long tails; in this case it is more consistent to use an (L_1) norm regularization scheme.
However, above SH degree 9 the GRIMM SA is controlled by the applied regularization and probably drops too rapidly to be consistent with the FF-hypothesis.
In addition, a mechanical regularization of the FE-SDIC measurements allows mechanically consistent fields to be evaluated, such as displacement and rotation fields that could be used as boundary conditions in the simulations.
