source_localization package

The main feature of the package source_localization is to estimate the quantity of pheromone emitted by the insects \(s_a\) by solving the following optimization problem:

\[s_a(x,y,t)=\underset{s(x,y,t)}{\arg\text{min}}~j(s)\text{ with } j(s)=j_{obs}(s)+j_{reg}(s)\]

with the cost function \(j\) of the following form:

\[j(s)=\|m\left(c(s)\right)-m_{obs}\|_{\mathbf{R}^{-1}}^2 + \sum_{i} \alpha_{reg,i} j_{reg,i}(s)\]

with \(\|m\left(c(s)\right)-m_{obs}\|_{\mathbf{R}^{-1}}^2\) the term of discrepancy between the data \(m_{obs}\) and the estimate computed using the pheromone propagation model \(m\left(c(s)\right)\), \(j_{reg,i}\) some regularization terms based on biological information and \(\alpha_{reg,i}\) the associated weight coefficient.

To solve such optimization problems, the package includes:

  • a submodule cost that contains the cost function \(j\), tools to construct the cost function and to minimize it;

  • a submodule obs that contains all the features related to the sensors and the observations, including the observations \(m_{obs}\) and the observation operator \(c\mapsto m(c)\);

  • a submodule control containing the control variable to optimize \(s(x,y,t)\) and all its prior known features;

  • a submodule population_dynamique containing population dynamic models used as prior knowledge of the control variable and their implementation;

  • a submodule adjoint_convection_diffusion_2D that contains the adjoint model used to compute the gradient of the cost function;

  • submodules gradient_descent and proximal_gradient that contain algorithms to solve the optimization problem.