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".
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== Running the HDMR Sweep ==Â 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 run, you can see the new values of the [[optimization]] [[variables]] as well as the computed error. After the [[optimization]] convergessweep process is finished, all the [[optimization]] [[variables]] are updated an HDMR file with their optimal values by defaulta '''. You can disable this feature by unchecking HDM''' file extension is added to your project's folder, which contains all the box labeled Update [[Variables]] with Optimal Values at Completionmonomial coefficients of your HDMR model.