Skip to content
Snippets Groups Projects
Commit 9a81d75e authored by Bas Nijholt's avatar Bas Nijholt
Browse files

add figure

parent 9f42b003
No related branches found
No related tags found
No related merge requests found
Pipeline #21370 passed
File added
...@@ -36,10 +36,13 @@ If the goal of the simulation is to approximate a continuous function with the l ...@@ -36,10 +36,13 @@ If the goal of the simulation is to approximate a continuous function with the l
Such a sampling strategy would trivially speedup many simulations. Such a sampling strategy would trivially speedup many simulations.
One of the most significant complications here is to parallelize this algorithm, as it requires a lot of bookkeeping and planning ahead. One of the most significant complications here is to parallelize this algorithm, as it requires a lot of bookkeeping and planning ahead.
![The algorithm.
](figures/algo.pdf){#fig:algo}
#### We describe a class of algorithms relying on local criteria for sampling, which allow for easy parallelization and have a low overhead. #### We describe a class of algorithms relying on local criteria for sampling, which allow for easy parallelization and have a low overhead.
Due to parallelization, the algorithm should be local, meaning that the information updates are only in a region around the newly calculated point. Due to parallelization, the algorithm should be local, meaning that the information updates are only in a region around the newly calculated point.
Additionally, the algorithm should also be fast in order to handle many parallel workers that calculate the function and request new points. Additionally, the algorithm should also be fast in order to handle many parallel workers that calculate the function and request new points.
A simple example is greedily optimizing continuity of the sampling by selecting points according to the distance to the largest gaps in the function values. A simple example is greedily optimizing continuity of the sampling by selecting points according to the distance to the largest gaps in the function values, as in Fig. @fig:algo.
For a one-dimensional function with three points known (its boundary points and a point in the center), the following steps repeat itself: For a one-dimensional function with three points known (its boundary points and a point in the center), the following steps repeat itself:
(1) keep all points $x$ sorted, where two consecutive points define an interval, (1) keep all points $x$ sorted, where two consecutive points define an interval,
(2) calculate the Euclidean distance for each interval (see $L_{1,2}$ in Fig. @fig:loss_1D), (2) calculate the Euclidean distance for each interval (see $L_{1,2}$ in Fig. @fig:loss_1D),
......
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment