Running C++

In this tutorial we show how Korali can be used with c++. For this we optimize a model with the solver CMA-ES and LM-CMA. Here we want to find the parameters \(v = (Intensity , PosX, PosY, Sigma)\) that maximize the posterior in a Bayesian problem.

How to run the example

Run the Makefile to compile the executables. Then you can run am example, e.g. ./run-cmaes This should output information about the process and result of the optimization.

Short explanation

The problem to be solved is a static heat conduction problem, with a candle as static heat source. The variables Intensity , PosX, PosY are position and intensity of the candle. Sigma is the standard deviation of the noise in the Additive Normal noise model - the noise \(\epsilon\) that is added to the function \(f\) (heat2Dsolver, see below) to obtain the measured temperature at each data point.

Computational Model and Data Points

First, we create the Korali engine and an experiment that we will configure,

auto k = korali::Engine();
auto e = korali::Experiment();
auto p = heat2DInit(&argc, &argv);

Here, heat2DInit, defined in [heat2d.cpp](model/heat2d.cpp), returns the data points (triples (xPos, yPos, refTemp)) as p. We model refTemp as a function of xPos and yPos (a function whose parameters \(v1\) we want to determine), in addition to some noise: \(refTemp(xPos, yPos) = f_{v1}(xPos, yPos) + \epsilon\). The distribution of the noise \(\epsilon\) depends on parameters \(v2\). We want to estimate \(v = (v1, v2)\).

We next set the problem type to Bayesian inference, assign the objective values (refTemp values) of our data as Reference Data and set the computational model to the function heat2DSolver (our f above), defined in [heat2d.cpp](model/heat2d.cpp),

e["Problem"]["Type"] = "Evaluation/Bayesian/Inference/Reference";
e["Problem"]["Likelihood Model"] = "Additive Normal";
e["Problem"]["Reference Data"] = p.refTemp;
e["Problem"]["Computational Model"] = &heat2DSolver;

Function [heat2DSolver](model/heat2d.cpp) internally already has access to the data points created by heat2DInit. The function calculates temperature values iteratively on a grid over the domain of xPos and yPos, using the Gauss-Seidel method. To get the temperature values at the data points and set them as Reference Evaluations, heat2DSolver finds a point on the grid close to each data point and returns the temperature value at this grid point.


Then, we decide on CMAES as solver and configure its parameters,

e["Solver"]["Type"] = "Optimizer/CMAES";
e["Solver"]["Population Size"] = 32;
e["Solver"]["Termination Criteria"]["Max Generations"] = 100;

Variables and Prior Distributions

We then need to define four variables, as well as a prior distribution for each of them,

e["Distributions"][0]["Name"] = "Uniform 0";
e["Distributions"][0]["Type"] = "Univariate/Uniform";
e["Distributions"][0]["Minimum"] = 10.0;
e["Distributions"][0]["Maximum"] = 60.0;

e["Distributions"][1]["Name"] = "Uniform 1";
e["Distributions"][1]["Type"] = "Univariate/Uniform";
e["Distributions"][1]["Minimum"] = 0.0;
e["Distributions"][1]["Maximum"] = 0.5;

e["Distributions"][2]["Name"] = "Uniform 2";
e["Distributions"][2]["Type"] = "Univariate/Uniform";
e["Distributions"][2]["Minimum"] = 0.6;
e["Distributions"][2]["Maximum"] = 1.0;

e["Distributions"][3]["Name"] = "Uniform 3";
e["Distributions"][3]["Type"] = "Univariate/Uniform";
e["Distributions"][3]["Minimum"] = 0.0;
e["Distributions"][3]["Maximum"] = 20.0;

e["Variables"][0]["Name"] = "Intensity";
e["Variables"][0]["Bayesian Type"] = "Computational";
e["Variables"][0]["Prior Distribution"] = "Uniform 0";
e["Variables"][0]["Initial Mean"] = 30.0;
e["Variables"][0]["Initial Standard Deviation"] = 5.0;

e["Variables"][1]["Name"] = "PosX";
e["Variables"][1]["Bayesian Type"] = "Computational";
e["Variables"][1]["Prior Distribution"] = "Uniform 1";
e["Variables"][1]["Initial Mean"] = 0.25;
e["Variables"][1]["Initial Standard Deviation"] = 0.01;

e["Variables"][2]["Name"] = "PosY";
e["Variables"][2]["Bayesian Type"] = "Computational";
e["Variables"][2]["Prior Distribution"] = "Uniform 2";
e["Variables"][2]["Initial Mean"] = 0.8;
e["Variables"][2]["Initial Standard Deviation"] = 0.1;

e["Variables"][3]["Name"] = "Sigma";
e["Variables"][3]["Bayesian Type"] = "Statistical";
e["Variables"][3]["Prior Distribution"] = "Uniform 3";
e["Variables"][3]["Initial Mean"] = 10.0;
e["Variables"][3]["Initial Standard Deviation"] = 1.0;

Running the Optimization

Finally, we call the run() routine to run the optimization, to find those parameters v that are most likely, using Bayes rule: We want to find v that maximize \(P(v|X) = P(X|v)*prior(v)\), i.e, the likelihood of the data times their prior.;