digeo.optim.mesh_gd#

digeo.optim.mesh_gd(mesh, x, loss_func, use_line_search=True, max_iter=100, lr=1.0, tol=1e-06, min_rel_improvement=1e-05, patience=3)[source]#

Gradient descent optimiser with line search and early stopping.

Parameters:

  • mesh (Mesh) – The mesh used for the optimisation.

  • x (MeshPointBatch) – The initial points on the mesh to optimize.

  • loss_func (MeshLossFunc) – The loss function to optimize.

  • use_line_search (bool) – Whether to use line search to find the optimal step size at each iteration (default: True).

  • max_iter (int) – The maximum number of iterations (default: 100).

  • lr (float) – The initial learning rate for the line search (default: 1.0).

  • tol (float) – The tolerance for the stopping criterion based on the gradient norm (default: 1e-6).

  • min_rel_improvement (float) – The minimum relative improvement in the loss for early stopping (default: 1e-5).

  • patience (int) – The number of iterations to wait for an improvement before stopping (default: 3).

Returns:

  • x’ (MeshPointBatch) – The optimized points on the mesh.

  • logs (dict[str, Any]) – A dictionary containing the information to log, where the keys are the names of the metrics and the values are the corresponding values to log. By default, the logs contain:

    • "loss" (List[float]): The loss value at each iteration.

    • "time" (float): The total time taken for the optimization.

    • "function_calls" (List[int]): The total number of function calls at each iteration.

    • "step_size" (List[float]): The step size at each iteration.

    • "mean_dir" (List[float]): The mean direction norm at each iteration.

Return type:

Tuple[MeshPointBatch, dict]