# Evolutionary Statistical System Based on Novelty Search:
## 1 Introduction  
The prediction of propagation of natural phenomena is a highly challenging task with important applications, such as prevention and monitoring of the behavior of forest fires, which affect millions of hectares worldwide every year, with devastating consequences on flora and fauna, as well as human health, activities, and economy [1]. In most cases, forest fires are human-caused, although there are also natural causes, such as lightning, droughts, or heat waves. Additionally, climate change has effects, such as high temperatures or extreme droughts, that exacerbate the risk of fires. The prevalence of these phenomena makes it crucial to have methods that can aid with firefighting efforts, e.g., prevention of fires and monitoring and analysis of fire spread on the ground. A basic tool for these analyses are fire simulators, which use computational propagation models in order to predict how the fire line progresses during a period of time. Examples of simulators are BEHAVE [2], FARSITE [3], fireLib [4], BehavePlus [5], and FireStation [6]. Fire spread prediction tasks can be performed either in real time or as a precautionary measure, for example, in order to assess areas of higher risk, or for the development of contingency plans that allocate resources according to predicted patterns of behavior. Unfortunately, the propagation models for fire spread prediction involve a high degree of uncertainty. On the one hand, modelling natural phenomena involves the possibility of errors due to characteristics inherent to the computational methods used. On the other hand, the simulators require the definition of a number of environmental parameters, also called a _scenario_, and although these values can greatly influence the results of a prediction, they are often not known beforehand, cannot be provided in real time, or may be susceptible to measuring errors. These difficulties result in predictions that may be far from the actual spread, especially when using what we call a \"classical prediction\", i.e., a single prediction obtained by simulating the fire with only one set of parameters. Nowadays, there are several frameworks that follow strategies for reducing this uncertainty based on the combination of results from multiple simulations. There are solutions categorized as _Data-Driven Methods_ (DDMs), which perform a number of simulations taking different scenarios as input. From these results, the system chooses the set of parameters that obtained a better prediction in the past and uses it as input for the prediction of the future behavior of the fire. Examples of this strategy are found in [7, 8]. While there is an improvement over the single-simulation strategy, these methods still use a single scenario for the prediction. This can be a great limitation due to the uncertainty in the dynamic conditions of the fire, and the possibility of errors; that is, a good scenario for a previous step might not be as good for the next. For example, a scenario might have yielded good results only by chance, or it may be an anomalous case that does not generalize well to the fire progress. Other approaches have set out to overcome this problem by combining results from multiple simulations and using these combined results for producing a prediction. Such methods are called _Data-Driven Methods with Multiple Overlapping Solutions_, or DDM-MOS. We provide a summary of the taxonomy of several methods in Figure 1. Except for the Classical Prediction, all methods shown in the figure belong in the DDM-MOS category. One of these solutions is the _Statistical System for Forest Fire Management_, or \(S^{2}F^{2}M\)[9]. This system uses a factorial experiment of the values of variables for choosing scenarios to evaluate, which consists of an exhaustive combination of values based on a discretization of the environmental variables. This strategy presents the challenge of having to deal with a large space of possible scenarios, which makes simulation prohibitive.