Because the full-order model is ill-conditioned, reduced-order models are constructed using time-scale decomposition arguments.
What is interesting is an excellent match between the predicted and simulated formations for the anisotropy parameter ((F_{alpha beta }=0.15)), for which the corresponding phase-field model is ill-posed (middle columns).
The estimated B-splines exhibit very moderate accelerations (in the case of the full model, see Fig. 6), and it may be possible to simplify the parameterisation of the time dependence in future models, e.g. to an exponential saturation in time as this is the expected behaviour of the VFM instrument sensitivity; however, an exponential model is ill-conditioned on the time span of data used here.
Linear regression model is ill-conditioned when the number of variables (genes) exceeds the number of observations (conditions), resulting in most of the regression coefficients taking on values of zero.
Using a Monte Carlo style assessment of parameter uncertainty, it was shown that the simple three-parameter model was ill-posed when calibrated solely to the streamflow response.
The difficulty with this approach for optical data is because each of these inverse models is ill-posed (which means that there is no unique solution), the solution to one particular subject might be different from a second subject.
This makes them more effective in applications where existing models are ill-defined and not reliable enough.
Some of the properties we study, such as the structural promiscuity of a function, are not easy to infer from such a data set, nor can they be inferred from models of protein folding such as lattice proteins, because such models are ill-suited to study protein function.
Since the models are ill-posed, there are infinite equally valid solutions that explain the data.
Unfortunately it appears that most current plant growth models are ill-suited to perform such a task because growth is typically modelled as a function of carbon assimilation (mainly affected by radiation interception, temperature and possibly water and N uptake) but not as a function of other growth-limiting factors.
