# Dynamic Line Scan Thermography Parameter Design via Gaussian Process Emulation
## 4 Discussion  
Both the RMSE and the average standard deviation show an initial steep decline that gradually flatlines. All our experiments have shown to converge to the same values after enough iterations. These curves support the decision making process whether or not to continue to add more data points (costly simulations). For our application, one could conclude that after 350 iterations the RMSE and the standard deviation are sufficiently low enough and do not change significantly anymore. The total amount of iterations needed to train the Gaussian process such that it can approximate the simulations up to an adequate level, depends on the application itself. It is a function of the available computational budget and the amount of uncertainty that can be tolerated. Similarly, generating a response surface is also subjective in the sense of deciding when a surrogate has a sufficient resolution and accuracy for the specified application. Therefore this manuscript does not focus on the exact numbers or percentage of data points needed to approximate the response surface. Simulators and emulators are models of an underlying truth and as such nothing more than an approximation. This means that one has to be prudent about the outcomes of such models. For instance, it is possible for the model to predict values that do not correspond with reality or, even worse, that do not have any physical meaning. For instance, we noticed that for some test points (points were we make predictions) far away from the data, it is possible to obtain negative values for the temperature difference, even though the data only contained positive values. This issue can be dealt with in two ways. First, one could implement constraints on the model. In our case we could alter the covariance function, such that only positive values can be predicted by the model. This is an approach thoroughly explained in [23]. Second, in this research, we chose the Gaussian process for the underlying machine learning model. By following the Bayesian paradigm [9], this stochastic model makes predictions that are not just numerical values (in our case for the temperature difference). They are also accompanied by a variance. As such, each prediction for every test point is in fact a normal distribution. The variance can be interpreted as a measurement of uncertainty about the prediction. This extra information should be taken into account when evaluating the predictions. As mentioned throughout the text, several optimisations could further improve the performance of the model. They were not investigated in this work, because we wanted to restrict ourselves to a basic implementation of the core idea of approximating dynamic line scan thermography parameter design via emulation. We consider these to be future work. First, the initial sampled points were drawn uniformly from the input space. Several alternatives are described in the literature [12; 16; 17]. As the total number of sampled points increases, the influence of the initial points becomes less important. Still, on very tight computational budgets, this could become a factor of interest. Second, the Uncertainty Sampling method sometimes favours points on the boundary of the input space. This