Overview Contents Previous Next Geant4 User's Guide
For Application Developers
Toolkit Fundamentals

3.7 Event Biasing Techniques

3.7.1 Scoring, Geometrical Importance Sampling and Weight Roulette

Geant4 provides event biasing techniques which may be used to save computing time in such applications as the simulation of radiation shielding. These are geometrical splitting and Russian roulette (also called geometrical importance sampling), and weight roulette. A basic scoring system is also provided in order to monitor the sampling. In this chapter, it is assumed that the reader is familiar with both the usage of Geant4 and the concepts of importance sampling. More detailed documentation may be found at [1]. A detailed description of different use-cases which employ the sampling and scoring techniques can be found at [2].
The goals of the scoring technique are to: Standard scoring must be provided for quantities such as tracks entering a cell, average weight of entering tracks, energy of entering tracks, and collisions inside the cell.
The purpose of importance sampling is to save computing time by sampling less often the particle histories entering "less important" geometry regions, and more often in more "important" regions. Given the same amount of computing time, an importance-sampled and an analogue-sampled simulation must show equal mean values, while the importance-sampled simulation will have a decreased variance.
The implementation of scoring is independent of the implementation of importance sampling. However both share common concepts. Scoring and importance sampling apply to particle types chosen by the user.
Examples on how to use scoring and importance sampling may be found in examples/extended/biasing and examples/advanced/Tiara. Geometries

The kind of scoring referred to in this note and the importance sampling apply to spatial cells provided by the user.

A cell is a physical volume (further specified by it's replica number, if the volume is a replica). Cells may be defined in two kinds of geometries:

  1. mass geometry: the geometry setup of the experiment to be simulated. Physics processes apply to this geometry.
  2. parallel-geometry: a geometry constructed to define the physical volumes according to which scoring and/or importance sampling is applied.
The user has the choice to score and/or sample by importance the particles of the chosen type, according to mass geometry or to parallel geometry. It is possible to utilize several parallel geometries in addition to the mass geometry. This provides the user with a lot of flexibility to define separate geometries for different particle types in order to apply scoring or/and importance sampling.

Limitations of "parallel" geometries Changing the Sampling

Samplers are higher level tools which perform the necessary changes of the Geant4 sampling in order to apply importance sampling and weight roulette. The samplers may also be used to apply scoring.

Scoring and variance reduction may be combined arbitrarily for chosen particle types and may be applied to the mass or to parallel geometries. The samplers support all combinations.

Different samplers are implemented for the mass and parallel geometries. Both implement the interface G4VSampler. G4VSampler allows the chosen combinations of scoring and variance reduction to be prepared and configures the sampling appropriately. To this end G4VSampler provides Prepare... methods and a Configure method:

 class G4VSampler
    virtual ~G4VSampler();
    virtual void PrepareScoring(G4VScorer *Scorer) = 0;
    virtual void PrepareImportanceSampling(G4VIStore *istore,
                                           const G4VImportanceAlgorithm 
                                           *ialg = 0) = 0;
    virtual void PrepareWeightRoulett(G4double wsurvive = 0.5,
                                      G4double wlimit = 0.25,
                                      G4double isource = 1) = 0;
    virtual void PrepareWeightWindow(G4VWeightWindowStore *wwstore,
                                     G4VWeightWindowAlgorithm *wwAlg = 0,
                                     G4PlaceOfAction placeOfAction = 
                                     onBoundary) = 0;
    virtual void Configure() = 0;
    virtual void ClearSampling() = 0;
    virtual G4bool IsConfigured() const = 0;

The methods for setting up the desired combination need specific information:

Each object of a sampler class is responsible for one particle type. The particle type is given to the constructor of the sampler classes via the particle type name, e.g. "neutron". Depending on the specific purpose, the Configure() of a sampler will set up specialized processes (derived from G4VProcess) for transportation in the parallel geometry, scoring, importance sampling and weight roulette for the given particle type. When Configure() is invoked the sampler places the processes in the correct order independent of the order in which user invoked the Prepare... methods.


Two classes implementing the interface G4VSampler are provided for the mass and a parallel geometry, respectively:

The constructors of both classes take the particle type name (e.g. "neutron") as an argument. In addition, the constructor of G4ParallelGeometrySampler needs a reference to the physical world volume of the parallel geometry. Scoring

Scoring is provided by a framework and is done according to particle type. Nevertheless it is also possible to score particles of different types into the same score. The framework may also be easily used for customized scoring.

Scoring may be applied to a mass or a parallel geometry. It is done with an object genericly called a scorer using a sampler described above. The scorer receives the information about every step taken by a particle of chosen type. This information consists of an object of the Geant4 kernel class G4Step and an object of the class G4GeometryCellStep provided specifically for the purpose of scoring and importance sampling. G4GeometryCellStep provides information about the previous and current "cell" of the particle track.

A "scorer" class derives from the interface G4VScorer. Users may create customized "scorers" or use the standard scoring.

Classes involved in the framework:

Note Importance Sampling

Importance sampling acts on particles crossing boundaries between "importance cells". The action taken depends on the importance values assigned to the cells. In general a particle history is either split or Russian roulette is played if the importance increases or decreases, respectively. A weight assigned to the history is changed according to the action taken.

The tools provided for importance sampling require the user to have a good understanding of the physics in the problem. This is because the user has to decide which particle types require importance sampled, define the cells, and assign importance values to the cells. If this is not done properly the results cannot be expected to describe a real experiment.

The assignment of importance values to a cell is done using an importance store described below.

An "importance store" with the interface G4VIStore is used to store importance values related to cells. In order to do importance sampling the user has to create an object (e.g. of class G4IStore) of type G4VIStore. The samplers may be given a G4VIStore. The user fills the store with cells and their importance values.

An importance store has to be constructed with a reference to the world volume of the geometry used for importance sampling. This may be the world volume of the mass or of a parallel geometry. Importance stores derive from the interface G4VIStore:

 class  G4VIStore
     virtual  ~G4VIStore();
     virtual G4double GetImportance(const G4GeometryCell &gCell) const = 0;
     virtual G4bool IsKnown(const G4GeometryCell &gCell) const = 0;
     virtual const G4VPhysicalVolume &GetWorldVolume() const = 0;

A concrete implementation of an importance store is provided by the class G4VStore. The public part of the class is:

 class G4IStore : public G4VIStore
     explicit G4IStore(const G4VPhysicalVolume &worldvolume);
     virtual ~G4IStore();
     virtual G4double GetImportance(const G4GeometryCell &gCell) const;
     virtual G4bool IsKnown(const G4GeometryCell &gCell) const;
     virtual const G4VPhysicalVolume &GetWorldVolume() const;
     void AddImportanceGeometryCell(G4double importance,
                              const G4GeometryCell &gCell);
     void AddImportanceGeometryCell(G4double importance,
                              const G4VPhysicalVolume &,
                                    G4int aRepNum = 0);
     void ChangeImportance(G4double importance,
                           const G4GeometryCell &gCell);
     void ChangeImportance(G4double importance,
                           const G4VPhysicalVolume &,
                                 G4int aRepNum = 0);
     G4double GetImportance(const G4VPhysicalVolume &,
                                  G4int aRepNum = 0) const ;
   private: .....

The member function AddImportanceGeometryCell() enters a cell and an importance value into the importance store. The importance values may be returned either according to a physical volume and a replica number or according to a G4GeometryCell. The user mus be aware of the interpretation of assigning importance values to a cell.


The different cases: The Importance Sampling Algorithm

Importance sampling supports using a customized importance sampling algorithm. To this end, the sampler interface G4VSampler may be given a pointer to the interface G4VImportanceAlgorithm:

 class G4VImportanceAlgorithm
     virtual ~G4VImportanceAlgorithm();
     virtual G4Nsplit_Weight Calculate(G4double ipre,
                                       G4double ipost,
                                       G4double init_w) const = 0;

The method Calculate() takes the arguments:

It returns the struct:

 class G4Nsplit_Weight

   G4int fN;
   G4double fW;

The user may have a customized algorithm used by providing a class inheriting from G4VImportanceAlgorithm.
If no customized algorithm is given to the sampler the default importance sampling algorithm is used. This algorithm is implemented in G4ImportanceAlgorithm. The Weight Window Technique

The weight window technique is a weight-based alternative to importance sampling:

In contrast to importance sampling this technique is not weight blind. Instead the technique is applied according to the particle weight with respect to the current energy-space cell.

Therefore the technique is convenient to apply in combination with other variance reduction techniques such as cross-section biasing and implicit capture.

A weight window may be specified for every cell and for several energy regions: space-energy cell .

Weight window concept

Weight window concept

The user specifies a lower weight bound W_L for every space-energy cell.

The energy-space cells are realized by G4GeometryCell as in importance sampling. The cells are stored in a weight window store defined by G4VWeightWindowStore:

 class  G4VWeightWindowStore {
    virtual  ~G4VWeightWindowStore();
    virtual G4double GetLowerWeitgh(const G4GeometryCell &gCell, 
			          G4double partEnergy) const = 0;
    virtual G4bool IsKnown(const G4GeometryCell &gCell) const = 0;
    virtual const G4VPhysicalVolume &GetWorldVolume() const = 0;

A concrete implementation is provided:

  class G4WeightWindowStore: public G4VWeightWindowStore {
     explicit G4WeightWindowStore(const G4VPhysicalVolume &worldvolume);
     virtual ~G4WeightWindowStore();
     virtual G4double GetLowerWeitgh(const G4GeometryCell &gCell, 
			             G4double partEnergy) const;
     virtual G4bool IsKnown(const G4GeometryCell &gCell) const;
     virtual const G4VPhysicalVolume &GetWorldVolume() const;
     void AddLowerWeights(const G4GeometryCell &gCell,
		          const std::vector<G4double> &lowerWeights);
     void AddUpperEboundLowerWeightPairs(const G4GeometryCell &gCell,
				         const G4UpperEnergyToLowerWeightMap&
     void SetGeneralUpperEnergyBounds(const 
         std::set<G4double, std::less<G4double> > & enBounds);

The user may choose equal energy bounds for all cells. In this case a set of upper energy bounds must be given to the store using the method SetGeneralUpperEnergyBounds. If a general set of energy bounds have been set AddLowerWeights can be used to add the cells.

Alternatively, the user may chose different energy regions for different cells. In this case the user must provide a mapping of upper energy bounds to lower weight bounds for every cell using the method AddUpperEboundLowerWeightPairs.

Weight window algorithms implementing the interface class G4VWeightWindowAlgorithm can be used to define a customized algorithm:

 class G4VWeightWindowAlgorithm {
    virtual ~G4VWeightWindowAlgorithm();
    virtual G4Nsplit_Weight Calculate(G4double init_w,
				      G4double lowerWeightBound) const = 0;

A concrete implementation is provided and used as a default:

 class G4WeightWindowAlgorithm : public G4VWeightWindowAlgorithm {
    G4WeightWindowAlgorithm(G4double upperLimitFaktor = 5,
			    G4double survivalFaktor = 3,
			    G4int maxNumberOfSplits = 5);
    virtual ~G4WeightWindowAlgorithm();
    virtual G4Nsplit_Weight Calculate(G4double init_w,
				      G4double lowerWeightBound) const;

The constructor takes three parameters which are used to: calculate the upper weight bound (upperLimitFaktor), calculate the survival weight (survivalFaktor), and introduce a maximal number (maxNumberOfSplits) of copies to be created in one go.

In addition, the inverse of the maxNumberOfSplits is used to specify the minimum survival probability in case of Russian roulette. The Weight Roulette Technique

Weight roulette (also called weight cutoff) is usually applied if importance sampling and implicit capture are used together. Implicit capture is not described here but it is useful to note that this procedure reduces a particle weight in every collision instead of killing the particle with some probability.

Together with importance sampling the weight of a particle may become so low that it does not change any result significantly. Hence tracking a very low weight particle is a waste of computing time. Weight roulette is applied in order to solve this problem.

The weight roulette concept

Weight roulette takes into account the importance "Ic" of the current cell and the importance "Is" of the cell in which the source is located, by using the ratio "R=Is/Ic".

Weight roulette uses a relative minimal weight limit and a relative survival weight. When a particle falls below the weight limit Russian roulette is applied. If the particle survives, tracking will be continued and the particle weight will be set to the survival weight.

The weight roulette uses the following parameters with their default values:

The following algorithm is applied:

If a particle weight "w" is lower than R*wlimit:

[1] Scoring, geometrical importance sampling and weight roulette in Geant4
[2] Use cases for importance biasing and scoring technique