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These depend on many unknown parameters that have to be inferred from experimental data.
Such a model usually suffers from many unknown parameters, boundary and initial conditions making the control system not robust.
Calibration of heterogeneous subsurface flow models usually leads to ill-posed nonlinear inverse problems, where too many unknown parameters are estimated from limited response measurements.
In the presence of sparse sampling, the analytical models often do not provide satisfactory results when there are so many unknown parameters.
Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.
Due to complex nature of the laser cladding process and presence of time-varying uncertainties, derivation of an accurate mathematical inverse dynamic model of the process is very difficult, and involves many unknown parameters.
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Third, whereas all the parameters of the PSHO model can be estimated using only coarse features of a measured expression level signal - period, amplitude, and offset, - the same may not hold for many nonlinear models because these generally have many more unknown parameters.
It is an ill-posed inverse problem with many unknown reservoir parameters that could be adjusted to obtain a match against a relatively smaller number of measurements.
To address this issue, discrete dynamical modeling has been used to provide an alternative way to qualitatively describe complex biological systems with many unknown kinetic parameters.
A common criticism of this approach has been that with so many unknown adjustable parameters it can easily fit any experimental data.
Model selection naturally extends the conventional hypothesis testing approach, and by accounting for uncertainty fairly and correctly, can be applied to systems with many unknown kinetic parameters (which are, in any case, inferred together with their respective uncertainties) (Liepe et al., 2013; Babtie et al., 2014).
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