17. Variance Reduction

Global variance reduction in OpenMC is accomplished by weight windowing techniques. OpenMC is capable of generating weight windows using either the MAGIC or FW-CADIS methods. Both techniques will produce a weight_windows.h5 file that can be loaded and used later on. In this section, we break down the steps required to both generate and then apply weight windows.

17.1. Generating Weight Windows with MAGIC

As discussed in the methods section, MAGIC is an iterative method that uses flux tally information from a Monte Carlo simulation to produce weight windows for a user-defined mesh. While generating the weight windows, OpenMC is capable of applying the weight windows generated from a previous batch while processing the next batch, allowing for progressive improvement in the weight window quality across iterations.

The typical way of generating weight windows is to define a mesh and then add an openmc.WeightWindowGenerator object to an openmc.Settings instance, as follows:

# Define weight window spatial mesh
ww_mesh = openmc.RegularMesh()
ww_mesh.dimension = (10, 10, 10)
ww_mesh.lower_left = (0.0, 0.0, 0.0)
ww_mesh.upper_right = (100.0, 100.0, 100.0)

# Create weight window object and adjust parameters
wwg = openmc.WeightWindowGenerator(
    method='magic',
    mesh=ww_mesh,
    max_realizations=settings.batches
)

# Add generator to Settings instance
settings.weight_window_generators = wwg

Notably, the max_realizations attribute is adjusted to the number of batches, such that all iterations are used to refine the weight window parameters.

With the WeightWindowGenerator instance added to the Settings, the rest of the problem can be defined as normal. When running, note that the second iteration and beyond may be several orders of magnitude slower than the first. As the weight windows are applied in each iteration, particles may be agressively split, resulting in a large number of secondary (split) particles being generated per initial source particle. This is not necessarily a bad thing, as the split particles are much more efficient at exploring low flux regions of phase space as compared to initial particles. Thus, even though the reported “particles/second” metric of OpenMC may be much lower when generating (or just applying) weight windows as compared to analog MC, it typically leads to an overall improvement in the figure of merit accounting for the reduction in the variance.

Warning

The number of particles per batch may need to be adjusted downward significantly to result in reasonable runtimes when weight windows are being generated or used.

At the end of the simulation, a weight_windows.h5 file will be saved to disk for later use. Loading it in another subsequent simulation will be discussed in the “Using Weight Windows” section below.

17.2. Generating Weight Windows with FW-CADIS and Random Ray

Weight window generation with FW-CADIS and random ray in OpenMC uses the same exact strategy as with MAGIC. An openmc.WeightWindowGenerator object is added to the openmc.Settings object, and a weight_windows.h5 will be generated at the end of the simulation. The only difference is that the code must be run in random ray mode. A full description of how to enable and setup random ray mode can be found in the Random Ray User Guide.

Note

It is a long term goal for OpenMC to be able to generate FW-CADIS weight windows with only a few tweaks to an existing continuous energy Monte Carlo input deck. However, at the present time, the workflow requires several steps to generate multigroup cross section data and to configure the random ray solver. A high level overview of the current workflow for generation of weight windows with FW-CADIS using random ray is given below.

1. Begin by making a deepy copy of your continuous energy Python model and then convert the copy to be multigroup and use the random ray transport solver. The conversion process can largely be automated as described in more detail in the random ray quick start guide, summarized below:

   # Define continuous energy model
   ce_model = openmc.pwr_pin_cell() # example, replace with your model
   
   # Make a copy to convert to multigroup and random ray
   model = copy.deepcopy(ce_model)
   
   # Convert model to multigroup (will auto-generate MGXS library if needed)
   model.convert_to_multigroup()
   
   # Convert model to random ray and initialize random ray parameters
   # to reasonable defaults based on the specifics of the geometry
   model.convert_to_random_ray()
   
   # (Optional) Overlay source region decomposition mesh to improve fidelity of the
   # random ray solver. Adjust 'n' for fidelity vs runtime.
   n = 10
   mesh = openmc.RegularMesh()
   mesh.dimension = (n, n, n)
   mesh.lower_left = model.geometry.bounding_box.lower_left
   mesh.upper_right = model.geometry.bounding_box.upper_right
   model.settings.random_ray['source_region_meshes'] = [(mesh, [model.geometry.root_universe])]
   
   # (Optional) Improve fidelity of the random ray solver by enabling linear sources
   model.settings.random_ray['source_shape'] = 'linear'
   
   # (Optional) Increase the number of rays/batch, to reduce uncertainty
   model.settings.particles = 500
   

   If you need to improve the fidelity of the MGXS library, there is more information on generating multigroup cross sections via OpenMC in the random ray MGXS guide.

2. Add in a WeightWindowGenerator in a similar manner as for MAGIC generation with Monte Carlo and set the method attribute set to "fw_cadis":

   # Create weight window object and adjust parameters, using the same mesh
   # we used for source region decomposition
   wwg = openmc.WeightWindowGenerator(
       method='fw_cadis',
       mesh=mesh
   )
   
   # Add generator to openmc.settings object
   settings.weight_window_generators = wwg
   

Warning

If using FW-CADIS weight window generation, ensure that the selected weight window mesh does not subdivide any source regions in the problem. This can be ensured by using the same mesh for both source region subdivision (i.e., assigning to model.settings.random_ray['source_region_meshes']) and for weight window generation.

3. When running your multigroup random ray input deck, OpenMC will automatically run a forward solve followed by an adjoint solve, with a weight_windows.h5 file generated at the end. The weight_windows.h5 file will contain FW-CADIS generated weight windows. This file can be used in identical manner as one generated with MAGIC, as described below.

17.3. Using Weight Windows

To use a weight_windows.h5 weight window file with OpenMC’s Monte Carlo solver, the Python input just needs to load the h5 file:

settings.weight_window_checkpoints = {'collision': True, 'surface': True}
settings.survival_biasing = False
settings.weight_windows = openmc.WeightWindowsList.from_hdf5('weight_windows.h5')
settings.weight_windows_on = True

The WeightWindowGenerator instance is not needed to load an existing weight_windows.h5 file. Inclusion of a WeightWindowGenerator instance will cause OpenMC to generate new weight windows and thus overwrite the existing weight_windows.h5 file. Weight window mesh information is embedded into the weight window file, so the mesh does not need to be redefined. Monte Carlo solves that load a weight window file as above will utilize weight windows to reduce the variance of the simulation.