https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Yildiz_et_al_2022aYildiz et al 2022a - Revision history2026-04-22T21:17:18ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=Yildiz_et_al_2022a&diff=262720&oldid=prevMove page script: Move page script moved page Yildiz et al 1970a to Yildiz et al 2022a2022-11-25T15:06:33Z<p>Move page script moved page <a href="/public/Yildiz_et_al_1970a" class="mw-redirect" title="Yildiz et al 1970a">Yildiz et al 1970a</a> to <a href="/public/Yildiz_et_al_2022a" title="Yildiz et al 2022a">Yildiz et al 2022a</a></p>
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</td></tr></table>Move page scripthttps://www.scipedia.com/wd/index.php?title=Yildiz_et_al_2022a&diff=259974&oldid=prevJSanchez: JSanchez moved page Draft Sanchez Pinedo 384990592 to Yildiz et al 1970a2022-11-22T13:06:17Z<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_384990592" class="mw-redirect" title="Draft Sanchez Pinedo 384990592">Draft Sanchez Pinedo 384990592</a> to <a href="/public/Yildiz_et_al_1970a" class="mw-redirect" title="Yildiz et al 1970a">Yildiz et al 1970a</a></p>
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</td></tr></table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Yildiz_et_al_2022a&diff=259973&oldid=prevJSanchez at 13:06, 22 November 20222022-11-22T13:06:11Z<p></p>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Yildiz_et_al_2022a&diff=259971&oldid=prevJSanchez at 13:06, 22 November 20222022-11-22T13:06:09Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 13:06, 22 November 2022</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Advanced applications of multi-fidelity surrogate modelling techniques provide significant improvements in optimization and uncertainty quantification studies in many engineering fields. Multi-fidelity surrogate modelling can efficiently save the design process from the computational time burden caused by the need for numerous computationally expensive simulations. However, no consensus exists about which multi-fidelity surrogate modelling technique usually exhibits superiority over the other methods given for certain conditions. Therefore, the present paper focuses on assessing the performances of the Gaussian Process-based multi-fidelity methods across selected benchmark problems, especially chosen to capture diverse mathematical characteristics, by experimenting with their learning processes concerning different performance criteria. In this study, a comparison of Linear-Autoregressive Gaussian Process and NonlinearAutoregressive Gaussian Process methods is presented by using benchmark problems that mimic the behaviour of real engineering problems such as localized behaviours, multi-modality, noise, discontinuous response, and different discrepancy types. Our results indicate that the considered methodologies were able to capture the behaviour of the actual function sufficiently within the limited amount of budget for 1-D cases. As the problem dimension increases, the required number of training data increases exponentially to construct an acceptable surrogate model. Especially in higher dimensions, i.e. more than 5-D, local error metrics reveal that more training data is needed to attain an efficient surrogate for Gaussian Process based strategies.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Advanced applications of multi-fidelity surrogate modelling techniques provide significant improvements in optimization and uncertainty quantification studies in many engineering fields. Multi-fidelity surrogate modelling can efficiently save the design process from the computational time burden caused by the need for numerous computationally expensive simulations. However, no consensus exists about which multi-fidelity surrogate modelling technique usually exhibits superiority over the other methods given for certain conditions. Therefore, the present paper focuses on assessing the performances of the Gaussian Process-based multi-fidelity methods across selected benchmark problems, especially chosen to capture diverse mathematical characteristics, by experimenting with their learning processes concerning different performance criteria. In this study, a comparison of Linear-Autoregressive Gaussian Process and NonlinearAutoregressive Gaussian Process methods is presented by using benchmark problems that mimic the behaviour of real engineering problems such as localized behaviours, multi-modality, noise, discontinuous response, and different discrepancy types. Our results indicate that the considered methodologies were able to capture the behaviour of the actual function sufficiently within the limited amount of budget for 1-D cases. As the problem dimension increases, the required number of training data increases exponentially to construct an acceptable surrogate model. Especially in higher dimensions, i.e. more than 5-D, local error metrics reveal that more training data is needed to attain an efficient surrogate for Gaussian Process based strategies.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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</table>JSanchezhttps://www.scipedia.com/wd/index.php?title=Yildiz_et_al_2022a&diff=259969&oldid=prevJSanchez at 13:06, 22 November 20222022-11-22T13:06:08Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 13:06, 22 November 2022</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">                                </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Summary==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Advanced applications of multi-fidelity surrogate modelling techniques provide significant improvements in optimization and uncertainty quantification studies in many engineering fields. Multi-fidelity surrogate modelling can efficiently save the design process from the computational time burden caused by the need for numerous computationally expensive simulations. However, no consensus exists about which multi-fidelity surrogate modelling technique usually exhibits superiority over the other methods given for certain conditions. Therefore, the present paper focuses on assessing the performances of the Gaussian Process-based multi-fidelity methods across selected benchmark problems, especially chosen to capture diverse mathematical characteristics, by experimenting with their learning processes concerning different performance criteria. In this study, a comparison of Linear-Autoregressive Gaussian Process and NonlinearAutoregressive Gaussian Process methods is presented by using benchmark problems that mimic the behaviour of real engineering problems such as localized behaviours, multi-modality, noise, discontinuous response, and different discrepancy types. Our results indicate that the considered methodologies were able to capture the behaviour of the actual function sufficiently within the limited amount of budget for 1-D cases. As the problem dimension increases, the required number of training data increases exponentially to construct an acceptable surrogate model. Especially in higher dimensions, i.e. more than 5-D, local error metrics reveal that more training data is needed to attain an efficient surrogate for Gaussian Process based strategies.</ins></div></td></tr>
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