In the HDMR method, you run successive evaluations of a given function of one or more [[variables]] for a number of [[variables]] samples. Then you create an optimal monomial surface representation of the computed data as a function of those [[variables]]. The resulting simplified function is characterized by a finite number of monomial coefficients. Therefore, its computation is more faster and computationally efficient than the original functions.
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==Defining the HDMR Variables ==
[[Image:Variable32.png|thumb|500px|The HDMR Settings dialog.]]
To define the HDMR [[variables]], follow the procedure below:
* Open the Simulation '''Run Dialog''' of most of [[EM.Cube]]'s computational modules and select the '''HDMR''' option from the '''Simulation Mode''' dropdown list.
* Click the '''Settings''' button next to the simulation mode dropdown list to open up the HDMR Settings Dialog.
* On the left side of the "[[Variables]]" section of the dialog you see the "'Independent [[Variables]] Table", which lists all the available independent [[variables]] of your project. Select an independent variable from the table and use the Right Arrow (-->) button of the dialog to move it to the "HDMR [[Variables]] Table".
* Once the definition of your HDMR model is complete, click the '''OK''' button on the dialog to close it and return to the HDMR Settings dialog.
You will see your new HDMR added to the HDMR Model List table. You can modify a model definition using the {{key|Edit}} button of this dialog. You can also define more than one HDMR model at a time. Such models will be generated using the same simulation runs. However, it is recommended not to generate unrelated models together. In the example below, we have defined an HDMR model called "Resistance" for the real part of the Z11 [[parameters]] of a dipole antenna as a function of its length defined by an independent variable "L".
<table>
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<td> [[Image:Variable31.png|thumb|280px300px|Defining an objective HDMR model involving S Z parameters.]] </td><td> [[Image:Variable34.png|thumb|480px|Defining an objective involving antenna directivity.]] </td>
</tr>
</table>
[[Image:Variable34.png|thumb|550px|EM.Cube's Model dialog showing a the HDMR model "Resistance.HDM" generated by EM.Tempo's FDTD simulation engine.]] == Running an HDMR Sweep == After you define all of your HDMR [[variables]] and model(s), close the HDMR Settings dialog to return to the simulation Run dialog. When you click the {{key|Run }} button of the Simulation Run dialog to start the [[optimization]] HDMR sweep process, an Output Window pops up that reports the various stages of the [[optimization]] sweep loop and displays the progress or percentage of completion. At every runAfter the sweep process is finished, you an HDMR file with a '''.HDM''' file extension is added to your project's folder, which contains all the monomial coefficients of your HDMR model. You can see the your new values of the HDMR model [[optimizationEM.Cube]] 's Models Dialog, which you can open by clicking the '''Models''' button [[variablesFile:Models_icon.png]] as well as of the computed errorSimulate Toolbar or selecting '''Menu > Simulate > Models. After ..''' or using the keyboard shortcut {{key|Ctrl+L}}. Note that once you generate an HDMR model, you can use it everywhere in [[optimizationEM.Cube]] convergesjust like any standard or library function or like a functional, all tabular or Python model. In the above example, the syntax of your new custom function is Resistance(L) or Resistance(x). As you can see from the figure on the right, the current value of "Resistance" is about 115.2Ω because the argument of your HDMR function, i.e. "L", has a current value of 150mm, which can be verified in the [[optimizationVariables]] dialog. <p> </p>[[variablesImage:Back_icon.png|40px]] are updated with their optimal values by default. You can disable this feature by unchecking the box labeled Update '''[[VariablesParametric_Modeling,_Sweep_%26_Optimization | Back to Parametric Modeling, Sweep & Optimization]] with Optimal Values at Completion.'''