Factors determining modeling accuracy

Several attempts were performed to determine the accuracy of in silica prediction tools developed for lipophilicity (for a recent review, see [34]). The main factor limiting the accuracy of all predictive methods is the training sets used to generate the models, in terms of population and quality of the experimental data they contain. Since most of the methods proposed in commercial software were built with data available in the public domain, their accuracy can be expected to be comparable. Thus, in order to select the most suitable prediction tool, other criteria than accuracy have to be used such as the speed of the calculation for large databases, the price of commercial software or the application domain of the model. 

Two factors will determine the accuracy of the modeling. The first is the accuracy with which the dynamic mechanical properties of the constituent materials is known, and the second is the degree to which the effective modulus theory actually models the properties of the inhomogeneous material. 

A number of factors limit the accuracy with which parameters needed for the design of commercial equipment can be determined. The kinetic parameters may be affected by inaccurate accounting for laboratory reactor heat and mass transport, and hydrodynamics correlations for these are typically determined under nonreacting conditions at ambient temperature and pressure and with nonreactive model fluids and may not be applicable or accurate at reaction conditions. Experimental uncertainty including errors in analysis, measurement,... 

In evaluating a structure determination for accuracy and precision, it is usually prudent to inquire as to the quality of the electron density map according to which the final model was built, and to the properties and quality of the final model. The former question can be addressed in real space, that is, how good is the electron density map, and/or in reciprocal space, that is, how well determined were the phases, and how well measured the structure amplitudes that contributed to the map. The model, of course, can be judged by how well it predicts the diffraction intensities (the R factor), by how it explains chemical and biochemical questions, and how well it agrees with canonical stereochemical properties, such as bond lengths and angles. 

Since the dispersion of aerosols is driven primarily by advection, the sophistication and accuracy of the wind-field characterization provided to a model is the principal factor in determining the accuracy of the dispersion predictions provided by the model. This may range from ... 

FE mesh refinement, model representability, dimensionahty and adhesive non-linearity are the main influential factors that determine the accuracy of stress predictions to be anticipated from any FEM anaEysis. 

At the next level of accuracy, the confining surfaces are modeled as structured and the confined molecules are described at a united atom (UA) level. Although the surfaces are structured, the structure is typically simplified, most commonly FCC. The particles forming the surface may be allowed to vibrate around their lattice points however, this is not necessary and the same confined structure will be obtained if the particles are held stationary. This level of molecular model is very common and has led to the identification of important factors determining whether a fluid-solid transition occurs, as well as the nature of the formed solid. Here we provide examples of two important studies utilizing united atom molecular models, noting their specific contributions. 

Cost-effective, non-invasive, quantitative and simultaneous determination of low level Tlnuvin 770 (0.05 to 0.4 wt.%) and Irganox 225 (0.1 to 0.45 wt.%) contents in PP pellets by NIRS in diffuse reflection mode using MLWR and PLS spectroscopic models has been reported [287]. Seven samples were used for calibration and two for validation. Spectral bands attributable to Tinuvin 770 and Irganox 225 appear at 1560 nm and 1390 nm, respectively. For Tinuvin 770 a two factor PLS model from 1500 to 1600 nm was developed for Irganox 225 a four factor PLS model in the 1360 to 1460 nm region. A quotient-term multiple linear least-squares spectroscopic model was derived that characterises analyte concentration and corrects for spectroscopic differences within the matrix due to the extruder/pelletisers. Reported standard deviations of ca. 25 ppm for Tinuvin 770 and ca. 80 ppm for Irganox 225, or relative standard errors of 0.01 wt.% for Tinuvin 770 and 0.03 wt.% for Irganox 225, approach the accuracy of the reference analytical method. 

To put the errors in comparative models into perspective, we list the differences among strucmres of the same protein that have been detennined experimentally (Fig. 9). The 1 A accuracy of main chain atom positions corresponds to X-ray structures defined at a low resolution of about 2.5 A and with an / -factor of about 25% [192], as well as to medium resolution NMR structures determined from 10 interproton distance restraints per residue [193]. Similarly, differences between the highly refined X-ray and NMR structures of the same protein also tend to be about 1 A [193]. Changes in the environment... 

The precision of the rate constants as a function of temperature determines the standard deviations of the activation parameters. The absolute error, not the percentage error in the activation parameters, represents the agreement to the model, because of the exponential functions. If, for example, one wished to examine the values of AS for two reactions that were reported as -4 3 and 26 3 J mol 1K 1, then it should be concluded that the two are known to the same accuracy. Since AS and A// are correlated parameters, the uncertainty in AS will be about 1/Tav times that in A//. At ambient temperature this amounts to an approximate factor of three (that is, 1000/T, converting from joules for AS to kilojoules for A// ). Thus, the uncertainty in A//, 0 of 2.50 kJ mol 1 is consistent with the uncertainty in ASn of 7.21 J mol1 K-1 at Tav - 350 K. 

The CC2 model performes very different for static hyperpolarizabilities and for their dispersion. For methane, CC2 overestimates 70 by a similar amount as it is underestimated by CCS, thus giving no improvement in accuracy relative to the uncorrelated methods CCS and SCF. In contrast to this, the CC2 dispersion coefficients listed in Table 3 are by a factor of 3 - 8 closer to the CCSD values than the respective CCS results. The dispersion coefficients should be sensitive to the lowest dipole-allowed excitation energy, which determines the position of the first pole in the dispersion curve. The substantial improvements in accuracy for the dispersion coefficients are thus consistent with the good performance of CC2 for excitation energies [35,37,50]. 

The numerical accuracy of simulations performed using this model is affected by several factors. These include a) the degree of triangulation, b) the number of marching steps taken along the flow direction and c) the order of the polynomial basis function. Numerical accuracy improves as a, b and c increase, however the computational time can become excessive. Therefore, it was necessary to quantitatively determine the effects of these variables on numerical accuracy. 

This model is not precise, but does identify some of the factors that are important to indentation. Like the model, the hardness measurement process is not precise. At the micro-hardness level, the projected areas of indentations are measured, but this can only be done with about 10% accuracy. At the nano-indentation level, relative values can determined accurately, but absolute values are probably only about 10% accurate. 

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