## 1 Introduction  
Uncontrolled fires pose a significant threat to life and property. Predictions of the evolution of fire are essential for risk assessment and consequence mitigation. However, fires are controlled by complex chemical and physical processes (fluid mechanics, heat transfer, chemical kinetics, solid decomposition, etc. ), making detailed predictions difficult, time-consuming and often inaccurate. Furthermore, uncertainty assessment is complex because uncertainties can come from many directions that range from model parameters to the structure and assumptions embedded in the models [1]. Thermal decomposition of solid materials is one of the processes that are complex to model and carries significant uncertainties. All aspects of fire growth modeling require some representation of the thermal decomposition of condensed combustible materials. Earlier models relied on simple empirical laws that involved major simplifications and that were mainly based on heat transfer [2, 3]. A perfect example is the earlier treatment of ignition, where the inert heating approach was used towards establishing ignition criteria. Reviews of these simple ignition models can be found in classic textbooks [2, 3]. Among the most simplified representations of the onset of combustion are concepts, such as ignition temperatures. By defining such a criterion, the treatment of thermal decomposition is ultimately avoided, and ignition is defined purely as a thermal process [4]. An empirical determination of an ignition temperature (i.e., the surface temperature at ignition) allows the calculation of parameters, such as the time to ignition, or serves as inputs for simple flame spread models [2; 3]. More detailed formulations have avoided using an ignition temperature and characterized ignition using a critical mass-loss rate [2]. Once again, the mass-loss rate is expressed in thermal terms, and these models still do not consider a detailed analysis of thermal decomposition. An empirically determined critical mass flux for ignition serves as the ignition criterion. This ignition criterion has the advantage of using a quantity that can be measured effectively but also provides a direct link with physical concepts, such as flammability limits that an ignition temperature cannot deliver [3]. The introduction of high-performance computing has made these simplifications unnecessary resulting in the proliferation of many thermal decomposition models that serve as inputs to fire dynamics models [5; 6; 7; 8; 9]. The objective of these models goes beyond establishing ignition criteria and enables calculating the production of fuel during all stages of a fire. The production of fuel is a key parameter that serves as an input for any combustion model. Many computational tools have been developed, and each tool has its own specific approach to the modeling of these terms (FireFoam [5], GPyro [6], ThermaKin [7] or Pyroolis [8]), but a generic representation of the conservation law for fuel is represented by Equation (1):  
\[\frac{\partial}{\partial t}\bigg{(}\frac{\rho_{s}}{\rho_{s}(0)}\bigg{)}=\sum _{i=1}^{m}\Bigg{(}\sum_{\gamma\in P_{i}}\
u_{\gamma}r_{\gamma}-\sum_{\epsilon \in R_{i}}r_{\epsilon}\Bigg{)} \tag{1}\]  
In this equation \(\rho_{s}\) represents the mass volume of the solid, \(\rho_{s}(0)\) the initial mass volume of the solid, \(\
u_{\gamma}\) the stechiometric coefficient, \(r_{\gamma}\) is the production rate, \(r_{\epsilon}\) the consumption rate and \(m\) the number of species involved during the degradation process. \(P_{i}\) represents the reactions involving the production of the specie \(i\) and \(R_{i}\) represents those, which use the species \(i\) as a reactant. The key to solving Equation (1) is to determine the production and consumption rates. The first studies are attempting to determine the production and consumption rates, i.e., chemical kinetics, date to the 19 th century [10].