Available methods

All forward problems can be summarized by

$$O=[O_1, \ldots, O_{n_{obs}}]^T=f([p_1, \ldots, p_{n_{param}}]^T)$$ (2.3)

where $O_i$ are the observable values^2.1 and $p_i$ are the model parameters^2.2. Generally, a new function $L \in \Re$ is constructed ^2.3 which vanishes when $f$ is equal to $O$ . The inverse problem is equivalent to find the set of $p_1, \ldots, p_{n_{param}}$ that verifies

$$L([O_1, \ldots, O_{n_{obs}}]^T-f([p_1, \ldots, p_{n_{param}}]^T)=0$$ (2.4)

Practically, the minimum of $L$ is searched across the parameter space in different ways briefly explained in the following sections.