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<h1>Approximations - RBF & EBF</h1>

<table>
	<th colspan=2>Cantilever Beam Radial Basis Function (RBF) Approximation Example</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Radial Basis Function (RBF) approximation plugin
			to fit a model to data for a cantilever beam.  An optimization of the cantilever beam is
			performed using the resulting approximation model.
			<p><br>
			Load the model and review the approximation model:
			<ul>
				<li>Right click the optimization component and select 'Approximations'
				<li>Click 'View Data' to review data points, error analysis points, and coefficient fit data
				<li>Click 'Error Analysis...' to review goodness of fit for each response
				<li>Click 'Visualize...' to raise the approximation viewer;  adjust sliders, review 2D and
					3D graphs, zoom in on specific graphs for detailed visualization
			</ul>
			Run the model.  Compare optimization results to those obtained without the approximation model
			(run optimization examples or deactivate approximation model and re-run).
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamNLPQL-RBF.zmf">CantBeamNLPQL-RBF.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Approximation error analysis
				<li>Approximation interactive viewer
				<li>Optimization
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<p><br>
<table>
	<th colspan=2>Option Price Radial Basis Function (RBF) Approximation Example</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Radial Basis Function (RBF) approximation plugin
			to fit a model to data for option prices.  The test data and reference information
			for this example can be found at <a href="http://www.scientific-consultants.com/nnbd.html">
			http://www.scientific-consultants.com/nnbd.html</a>:
			<p><br>
			<i>"The data that follows consists of Black-Scholes option prices for volatility levels
			running from 20 percent to 200 percent, for time remaining running from 5 to 15 days, and
			for strike price running from 70 dollars to 130 dollars. The stock price was set to 100
			dollars and the interest rate to 0 percent when generating the data."</i>
			<p><br>
			The goal is to get an error of 0.01 dollars. Based on 20 random points cross validation
			the mean error in this RBF model is 0.0001 dollars and the maximum error is 0.002 dollars.
			<p><br>
			Load the model and review the approximation model:
			<ul>
				<li>Double click the approximation component
				<li>Click 'View Data' tab to review data points, error analysis points, and coefficient fit data
				<li>Click 'Error Analysis...' to review goodness of fit for each response
				<li>Click 'Visualize...' to raise the approximation viewer;  adjust sliders, review 2D and
					3D graphs, zoom in on specific graphs for detailed visualization
			</ul>
			NOTE: the data is built in to the approximation component in this model, and so the original
			data file is not needed here, but is included for reference:
			<a href="optionprice.txt">optionprice.txt</a>.
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="RBF-OptionPrice.zmf">RBF-OptionPrice.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Task, Approximation</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Approximation error analysis
				<li>Approximation interactive viewer
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<p><br>
<table>
	<th colspan=2>Airfoil Drag Radial Basis Function (RBF) Approximation Example</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Radial Basis Function (RBF) approximation plugin
			to fit a model to data for airfoil drag.
			<p><br>
			Load the model and review the approximation model:
			<ul>
				<li>Double click the approximation component
				<li>Click 'View Data' tab to review data points, error analysis points, and coefficient fit data
				<li>Click 'Error Analysis...' to review goodness of fit for each response
				<li>Click 'Visualize...' to raise the approximation viewer;  adjust sliders, review 2D and
					3D graphs, zoom in on specific graphs for detailed visualization
			</ul>
			NOTE: the data is built in to the approximation component in this model, and so the original
			data file is not needed here, but is included for reference:
			<a href="dragdata.txt">dragdata.txt</a>.
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="RBF-AirfoilDrag.zmf">RBF-AirfoilDrag.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Task, Approximation</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Approximation error analysis
				<li>Approximation interactive viewer
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<p><br>
<table>
	<th colspan=2>Noisy Data Radial Basis Function (RBF) Approximation Example</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Radial Basis Function (RBF) approximation plugin
			to fit a model to noisy data and demonstrates the noise smoothing control within RBF.
			<p><br>
			Load the model and review the approximation model:
			<ul>
				<li>Double click the approximation component
				<li>Click 'View Data' tab to review data points, error analysis points, and coefficient fit data
				<li>Click 'Error Analysis...' to review goodness of fit for each response
				<li>Click 'Visualize...' to raise the approximation viewer;  adjust sliders, review 2D and
					3D graphs, zoom in on specific graphs for detailed visualization
			</ul>
			NOTE: the data is built in to the approximation component in this model, and so the original
			data file is not needed here, but is included for reference:
			<a href="noisy.txt">noisy.txt</a>.
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="RBF-Noisy.zmf">RBF-Noisy.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Task, Approximation</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Approximation error analysis
				<li>Approximation interactive viewer
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<p><br>
<table>
	<th colspan=2>Uncorrelated Data Elliptical Basis Function (EBF) Approximation Example</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Elliptical Basis Function (EBF) approximation plugin
			to fit a model to a data where the response does not depend on one of the inputs.
			<p><br>
			Load the model and review the approximation model:
			<ul>
				<li>Double click the approximation component
				<li>Click 'View Data' tab to review data points, error analysis points, and coefficient fit data
				<li>Click 'Error Analysis...' to review goodness of fit for each response
				<li>Click 'Visualize...' to raise the approximation viewer;  adjust sliders, review 2D and
					3D graphs, zoom in on specific graphs for detailed visualization
			</ul>
			NOTE: the data is built in to the approximation component in this model, and so the original
			data file is not needed here, but is included for reference:
			<a href="uncorrelated.txt">uncorrelated.txt</a>.
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="EBF-Uncorrelated.zmf">EBF-Uncorrelated.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Task, Approximation</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Approximation error analysis
				<li>Approximation interactive viewer
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>

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