The error surfaces for each initial density are shown in Figure 6I J.
For each combination of D and q, we calculated Error DP (D, q) and compared the averaged simulated cell density profile with the corresponding averaged experimental profile to produce the error surfaces in Figure 5G H.
We also observe that our results are insensitive to the choice of D since the error surfaces in Figure 6I J appear to be independent of the value of D. The error surfaces indicate that for the experiments initialised with 20,000 cells, the optimal choice of q is between q=0.1 and q=0.6 and for experiments initialised with 30,000 cells the optimal range is between q=0.3 and q=0.6.
The error surfaces obtained using noisy data present the same shapes as seen for the noise-free data except that the error average is higher and points to a different global minimum, which however is essentially indistinguishable in value from the local optima (see Additional file 1 for details).
In the design of adaptive IIR filters, the multi-modal nature of the error surfaces can limit the use of gradient-based and other iterative search methods.
These models can interpolate among the different experimental conditions and can also describe the error surface when fitting life prediction models to the data.
Since the problem of the error surface of designing digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima.
Because the error surface of IIR filters is generally multi-modal, global optimisation techniques are required in order to avoid local minima and design efficient digital IIR filters.
In artificial neural networks (ANN), this translates to the minimization of the error surface during training such that misclassification is minimized during generalization.
The non-linear behaviour of the subsonic source can also cause a further problem, since the error surface experienced by the control system may exhibit local minima.
If the test is passed then the estimation can be considered reliable, in the sense that the optimisation search has reached a point on the error surface where the effect of nonlinearities is negligible.
