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<article role="main">
<section id="example-borehole">
<h1>Example: borehole<a class="headerlink" href="#example-borehole" title="Link to this heading">¶</a></h1>
<p>This test deals with the surrogate modeling of a Borehole function.
You will see how to check the quality of your regression model and perform sensitivity analysis via Sobol Indices</p>
<blockquote>
<div><p>BOREHOLE FUNCTION</p>
<dl class="simple">
<dt>Authors: Sonja Surjanovic, Simon Fraser University</dt><dd><p>Derek Bingham, Simon Fraser University</p>
</dd>
</dl>
<p>Questions/Comments: Please email Derek Bingham at <a class="reference external" href="mailto:dbingham%40stat.sfu.ca">dbingham<span>@</span>stat<span>.</span>sfu<span>.</span>ca</a>.</p>
<p>Copyright 2013. Derek Bingham, Simon Fraser University.</p>
<p>THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
FOR THE USE OF THIS SOFTWARE. If software is modified to produce
derivative works, such modified software should be clearly marked.
Additionally, this program is free software; you can redistribute it
and/or modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; version 2.0 of the License.
Accordingly, this program is distributed in the hope that it will be
useful, but WITHOUT ANY WARRANTY; without even the implied warranty
of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.</p>
<dl class="simple">
<dt>For function details and reference information, see:</dt><dd><p><a class="reference external" href="https://www.sfu.ca/~ssurjano/ishigami.html">https://www.sfu.ca/~ssurjano/ishigami.html</a></p>
</dd>
</dl>
</div></blockquote>
<p>no reference data given
Surrogate with AL - OMP for regression and Space-filling sequential exploitaiton scheme (no data)</p>
<section id="model-and-data">
<h2>Model and Data<a class="headerlink" href="#model-and-data" title="Link to this heading">¶</a></h2>
<div class="table-wrapper colwidths-given docutils container" id="id1">
<table class="docutils align-default" id="id1">
<caption><span class="caption-text">Pylink model</span><a class="headerlink" href="#id1" title="Link to this table">¶</a></caption>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Property</p></th>
<th class="head"><p>Setting</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Model type</p></td>
<td><p>Function</p></td>
</tr>
<tr class="row-odd"><td><p>Number of input parameters</p></td>
<td><p>8</p></td>
</tr>
<tr class="row-even"><td><p>Number of output parameters</p></td>
<td><p>1: flow rate [m$^3$/yr]</p></td>
</tr>
<tr class="row-odd"><td><p>Time- or space- dependency</p></td>
<td><p>??</p></td>
</tr>
<tr class="row-even"><td><p>MC reference</p></td>
<td><p>No</p></td>
</tr>
</tbody>
</table>
</div>
<div class="table-wrapper colwidths-given docutils container" id="id2">
<table class="docutils align-default" id="id2">
<caption><span class="caption-text">Priors</span><a class="headerlink" href="#id2" title="Link to this table">¶</a></caption>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Parameter</p></th>
<th class="head"><p>Distribution</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>r_w</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-odd"><td><p>L</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-even"><td><p>K_w</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-odd"><td><p>T_u</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-even"><td><p>T_l</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-odd"><td><p>H_u</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-even"><td><p>H_l</p></td>
<td><p>uniform</p></td>
</tr>
<tr class="row-odd"><td><p>r</p></td>
<td><p>lognormal</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="surrogate">
<h2>Surrogate<a class="headerlink" href="#surrogate" title="Link to this heading">¶</a></h2>
<div class="table-wrapper colwidths-given docutils container" id="id3">
<table class="docutils align-default" id="id3">
<caption><span class="caption-text">MetaModel settings</span><a class="headerlink" href="#id3" title="Link to this table">¶</a></caption>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Property</p></th>
<th class="head"><p>Setting</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>surrogate-type</p></td>
<td><p>aPCE</p></td>
</tr>
<tr class="row-odd"><td><p>associated model</p></td>
<td><p>‘borehole’</p></td>
</tr>
<tr class="row-even"><td><p>degree choices</p></td>
<td><p>max degree 5, q-norm truncation 1.0</p></td>
</tr>
<tr class="row-odd"><td><p>regression</p></td>
<td><p>OMP (Orthogonal matching pursuit)</p></td>
</tr>
</tbody>
</table>
</div>
<div class="table-wrapper colwidths-given docutils container" id="id4">
<table class="docutils align-default" id="id4">
<caption><span class="caption-text">Training choices</span><a class="headerlink" href="#id4" title="Link to this table">¶</a></caption>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Property</p></th>
<th class="head"><p>Setting</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Static sampling method</p></td>
<td><p>latin-hypercube</p></td>
</tr>
<tr class="row-odd"><td><p>Number of static samples</p></td>
<td><p>50</p></td>
</tr>
<tr class="row-even"><td><p>Number of total samples</p></td>
<td><p>300</p></td>
</tr>
<tr class="row-odd"><td><p>Number of samples per AL iteration</p></td>
<td><p>1</p></td>
</tr>
<tr class="row-even"><td><p>AL tradeoff scheme</p></td>
<td><p>None</p></td>
</tr>
<tr class="row-odd"><td><p>AL exploration method</p></td>
<td><p>latin-hypercube, n_candidates=5000, n_cand_groups=4</p></td>
</tr>
<tr class="row-even"><td><p>AL exploitation method</p></td>
<td><p>space-filling</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
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