# Introduction

The package **vle.recursive** allows to perform multi-simulations.
Based on the vle API, one can launch simulations
of an embedded model into a vle Dynamics. It provides:

- An API MetaManager for performing multi simulations
- A dynamic based on this API that can be configured by experimental conditions

The goals are:

- to provide both an API and a PDEVS dynamic for multi simulation, based on the same approach for configuration.
- to use the same approach for configuring MPI and thread parallelization provided into vle. Use either the vle implementation of vle (if available) or native threading parallelization.
- to facilitate the stochastic simulation.
- to provide simple tools for aggregating simulation results.
- to provide an alternative to multi simulation with R, with less memory allocation.

# Tutorial on vle.recursive package

Let us consider the SIR model as described on the Wikipedia page:

```
dS/dt = - beta * I * S;
dI/dt = beta * I * S - gamma * I;
dR/dt = gamma * I;
```

One also defines a simple stochastic version (called SIRnoise):

```
dS/dt = - beta * I * S * espilon1;
dI/dt = beta * I * S * epislon1 - gamma * I * epsilon2;
dR/dt = gamma * I * epsilon2;
epsilon1 ~ N(1, 0.3)
epsilon2 ~ N(1, 0.3)
```

The default parameters of the models are: S(0) = 99; I(0)=1; R(0)=0; beta=0.002; gamma=0.1. For the stochastic version, we also have a parameter ‘seed’ that gives the seed of the random number generator. Below, the result of the deterministic version with default paramters, for 60 integration time steps, are plotted into gvle.

- Performing multiple simulations: we consider 5 different values of S(0) and for each, we compute the mean value of the final states of S for 6 replicates with different ‘seed’ values.

```
namespace vr = vle::recursive;
namespace vv = vle::value;
vv::Map init;
init.addString("package","vle.recursive_test");
init.addString("vpz","SIRnoise.vpz");
//config output, 'mean' on replicate, 'all' on inputs
vv::Map& conf_out = init.addMap("output_Sfinal");
conf_out.addString("path", "view/top:SIRnoise.S");
conf_out.addString("integration", "last");
conf_out.addString("aggregation_replicate", "mean");
conf_out.addString("aggregation_input", "all");
//set 5 input values for S(0)
vv::Tuple& Svalues = init.addTuple(
"input_condSIRnoise.init_value_S", 5, 0.0);
Svalues[0] = 150;
Svalues[1] = 120;
Svalues[2] = 99;
Svalues[3] = 75;
Svalues[4] = 50;
//set 6 seeds for initializing the rng.
vv::Tuple& seeds = init.addTuple(
"replicate_condSIRnoise.init_value_seed", 6, 0.0);
seeds[0] = 45694;
seeds[1] = 55695;
seeds[2] = 65696;
seeds[3] = 85698;
seeds[4] = 95699;
vr::MetaManager meta;
vle::manager::Error err;
std::unique_ptr<vv::Map> res = meta.run(init, err);
if (err.code ==-1) {
std::cout << " error: " << err.message << "\n";
}
std::cout << " Results of final S: " << *res << "\n";
//(Sfinal, ((11.5526,22.2598,36.1712,51.3126,45.0968)))
```

- Evaluating the model on observations: let us consider we have at our disposal three observations of the number of infectious subjects, at times 20, 30 and 40. And we want to compute the mean square error of the simulations for different values of beta.

```
vv::Map init;
init.addString("package","vle.recursive_test");
init.addString("vpz","SIR.vpz");
//config output, mse on S
vv::Map& conf_out = init.addMap("output_mseI");
conf_out.addString("path", "view/top:SIR.I");
conf_out.addString("integration", "mse");
vv::Tuple& mseTimes = conf_out.addTuple("mse_times", 3,0.0);
mseTimes[0] = 20;
mseTimes[1] = 30;
mseTimes[2] = 40;
vv::Tuple& mseObs = conf_out.addTuple("mse_observations", 3,0.0);
mseObs[0] = 6;
mseObs[1] = 10;
mseObs[2] = 15;
conf_out.addString("aggregation_input", "all");
//set 3 input values for beta parameter
vv::Tuple& beta = init.addTuple("input_condSIR.init_value_beta", 3, 0.0);
beta[0] = 0.001;
beta[1] = 0.002;
beta[2] = 0.003;
vr::MetaManager meta;
vle::manager::Error err;
std::unique_ptr<vv::Map> res = meta.run(init, err);
if (err.code ==-1) {
std::cout << " error: " << err.message << "\n";
}
std::cout << " Mse on I for beta in (0.001,0.002,0.003): " << *res << "\n";
//(mseI, ((102.158,0.233604,228.278)))
```

(code of the tutorial into vle.recursive_test)

# The MetaManager API

The MetaManager is configured by a *vle::value::Map* provided by the user.
It can contains:

**vpz**(string) : it gives the name of the*vpz*file. It allows to identify together with*package*the embedded model.**package**(string) : it gives the name of the*package*where is located the embedded model. It allows to identify together with*vpz*the embedded model.**propagate_X**(*value::Value*, optional) : where X is of the form*condname.portname*, it specifies the value to set for all simulations to a port condition of the embedded model.**input_X**(*value::Set*or*value::Tuple*): where X is of the form*condname.portname*, it gives for one input the values to simulate. The size of the*value::Set*or*value::Tuple*defines the number*N*of combination inputs to simulate. For each input, it is required to have the same value of*N*.**replicate_X**(*value::Set*or*value::Tuple*, optional) where X is of the form*condname.portname*, it gives the values to simulate for the replicates (eg. seeds). The size of the*value::Set*or*value::Tuple*defines the number*M*of replicates to simulate. For each input, it is required to have the same value*M*. If no replicate is specified then*M=1*. Finally, the total number of simulations performed is*N***M*.**output_Y**(vle::value::Map) : where Y is an id for the output. The map should/could provide:**path**(string): is of the form*viewname/pathOfTheAtomicModel.ObsPort*. It identifies the column of outputs*ObsPort*computed by the atomic model*pathOfTheAtomicModel*and stored into the view*viewname*.**integration**(amongst ‘last’, ‘max’, ‘mse’ or ‘all’, default ‘last’): the type of temporal integration to perform. the output with id*X*. The string has the following form:**aggregation_replicate**(amongst ‘mean’, ‘variance’, ‘quantile’, default ‘mean’): It gives the type of aggregation to perform on the simulations replicates, once the temporal integration has been performed.**aggregation_input**(amongst ‘mean’, ‘max’, ‘all’ default ‘all’): It gives the type of aggregation to perform on the simulations inputs, once replicates have been aggregated.**mse_times**(*value::Tuple*): required only if integration=‘mse’. It gives times at which the mse_observations are given.**mse_observations**(*value::Tuple*): required only if integration=‘mse’. It gives the serie of observations for computing the MSE. mse_observations and mse_times must have the same length.**replicate_quantile**(*value::Double*): required only if aggregation_replicate=‘quantile’. It gives the quantile order to use for aggregating replicates.

**config_parallel_type**(string amongst*threads*,*mvle*and*single*; default*single*). It sets the type of parallelization to perform.**config_parallel_rm_files**(bool; default*true*). Used only if*config_parallel_type*is set to*mvle*. Simulation files created into directory*working_dir*are removed after analysis.**config_parallel_nb_slots**(int > 0). it gives the number of slots to use for parallelization.**working_dir**(string). Required only if*config_parallel_type*is set to*mvle*. It gives the working directory where are produced result file of single simulations.

# The MetaManager dynamic

The MetaManager atomic model has the following dynamic, implemented in PDEVS framework:

- If the conditions provide an initialization map for the MetaManager API, it performs the simulation of the experimental plan during the PDEVS initialization step, then it falls asleep for a given duration, then it outputs the results, and then falls asleep indefinitely.
- Each time it receives an experiment plan setting on its input port, it performs the simulation of the experiment plan, then it falls asleep for a duration, then it outputs the results and then falls asleep indefinitely. the results.

Configuring the dynamic consists in giving the elements required for the API configuration directly into conditions ports. Other configuration keys are:

**step_duration**(double, default 0). It gives the duration time, for the embedding simulator engine clock, required for the simulation of the experiment plan.