diff --git a/paper.md b/paper.md index e15b859ad7017f2b97c18c56b26958fcb75c91bc..34066866b731879ecbb087b55accf4ac03fc050f 100755 --- a/paper.md +++ b/paper.md @@ -325,13 +325,18 @@ For more details on how to use Adaptive, we recommend reading the tutorial insid # Possible extensions #### Anisotropic triangulation would improve the algorithm. -The current implementation of choosing the candidate point inside a simplex (triangle for 2D) with the highest loss, for the `LearnerND`, works by either picking a point (1) in the center of the simplex or (2) by picking a point on the longest edge of the simplex. +The current implementation of choosing the candidate point inside a simplex (triangle in 2D) with the highest loss, for the `LearnerND`, works by either picking a point (1) in the center of the simplex or (2) by picking a point on the longest edge of the simplex. The choice depends on the shape of the simplex, where the algorithm tries to create regular simplices. Alternatively, a good strategy is choosing points somewhere on the edge of a triangle such that the simplex aligns with the gradient of the function; creating an anisotropic triangulation[@dyn1990data]. This is a similar approach to the anisotropic meshing techniques mentioned in the literature review. -We have started to implement this feature in Adaptive, however, there are still some unsolved problems. +We have started to implement this feature in Adaptive, however, there some unsolved problems remain. #### Learning stochastic functions is a promising direction. +Stochastic functions frequently appear in numerical sciences. +Currently, Adaptive has a `AverageLearner` that samples a stochastic function with no degrees of freedom until a certain standard error of the mean is reached. +This is advantageous because no predetermined number of samples has to be set before starting the simulation. +Extending this learner to be able to deal with more dimensions would be a useful addition. +There is an effort to implement an `AverageLearner1D` and `AverageLearner2D`, however, it requires more work to make it reliable. #### Experimental control needs to deal with noise, hysteresis, and the cost for changing parameters.