https://vasp.at/wiki/index.php?action=history&feed=atom&title=ML_IALGO_LINREG
ML IALGO LINREG - Revision history
2026-04-15T07:57:31Z
Revision history for this page on the wiki
MediaWiki 1.43.8
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=31448&oldid=prev
Karsai at 07:25, 10 October 2025
2025-10-10T07:25:07Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:25, 10 October 2025</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{TAGDEF|ML_IALGO_LINREG|[integer]|1}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>{{TAGDEF|ML_IALGO_LINREG|[integer]<ins style="font-weight: bold; text-decoration: none;">}}</ins></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Description: This tag determines the algorithm that is employed to solve the system of linear equations in the ridge regression method for machine learning.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Description: This tag determines the algorithm that is employed to solve the system of linear equations in the ridge regression method for machine learning.</div></td></tr>
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Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20546&oldid=prev
Karsai: /* Related tags and articles */
2023-07-03T15:52:47Z
<p><span class="autocomment">Related tags and articles</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:52, 3 July 2023</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related tags and articles ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related tags and articles ==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_LMLFF}}, {{TAG|ML_MODE}}, {{TAG|ML_W1}}, {{TAG|ML_WTOTEN}}, {{TAG|ML_WTIFOR}}, {{TAG|ML_WTSIF}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>{{TAG|ML_LMLFF}}, {{TAG|ML_MODE}}, {{TAG|ML_W1}}, {{TAG|ML_WTOTEN}}, {{TAG|ML_WTIFOR}}, {{TAG|ML_WTSIF<ins style="font-weight: bold; text-decoration: none;">}}, {{TAG|ML_SIGW0</ins>}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{sc|ML_IALGO_LINREG|Examples|Examples that use this tag}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{sc|ML_IALGO_LINREG|Examples|Examples that use this tag}}</div></td></tr>
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Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20545&oldid=prev
Karsai at 15:52, 3 July 2023
2023-07-03T15:52:30Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:52, 3 July 2023</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*{{TAG|ML_IALGO_LINREG}}=2: QR factorization. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*{{TAG|ML_IALGO_LINREG}}=2: QR factorization. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*{{TAG|ML_IALGO_LINREG}}=3: Singular value decomposition. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*{{TAG|ML_IALGO_LINREG}}=3: Singular value decomposition. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*{{TAG|ML_IALGO_LINREG}}=4: Singular value decomposition with Tikhonov regularization. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>*{{TAG|ML_IALGO_LINREG}}=4: Singular value decomposition with Tikhonov regularization<ins style="font-weight: bold; text-decoration: none;">. The regularization can be controlled via {{TAG|ML_SIGW0}}</ins>. Usable with {{TAG|ML_MODE}} = ''REFIT'' and ''REFITBAYESIAN''.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For on the fly learning {{TAG|ML_MODE}} = ''TRAIN'' and reselection of local reference configurations {{TAG|ML_MODE}} = ''SELECT'', it is strictly necessary to use Bayesian regression ({{TAG|ML_IALGO_LINREG}}=1), since uncertainty estimates are only available for Bayesian regression. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For on the fly learning {{TAG|ML_MODE}} = ''TRAIN'' and reselection of local reference configurations {{TAG|ML_MODE}} = ''SELECT'', it is strictly necessary to use Bayesian regression ({{TAG|ML_IALGO_LINREG}}=1), since uncertainty estimates are only available for Bayesian regression. </div></td></tr>
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Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20544&oldid=prev
Karsai at 15:51, 3 July 2023
2023-07-03T15:51:45Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:51, 3 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24">Line 24:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed (for details please see [[Machine learning force field: Theory#Solution via regularized SVD|here]]. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>For {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed (for details please see [[Machine learning force field: Theory#Solution via regularized SVD|here]]<ins style="font-weight: bold; text-decoration: none;">)</ins>. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td></tr>
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Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20543&oldid=prev
Karsai at 15:51, 3 July 2023
2023-07-03T15:51:28Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:51, 3 July 2023</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>For {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed <ins style="font-weight: bold; text-decoration: none;">(for details please see [[Machine learning force field: Theory#Solution via regularized SVD|here]]</ins>. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20542&oldid=prev
Karsai at 15:48, 3 July 2023
2023-07-03T15:48:43Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:48, 3 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Line 8:</td>
<td colspan="2" class="diff-lineno">Line 8:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> || \mathbf{Y} - \mathbf{\Phi} \mathbf{w} || \rightarrow \mbox{min}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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> || \mathbf{Y} - \mathbf{\Phi} \mathbf{w} || \rightarrow \mbox{min}<ins style="font-weight: bold; text-decoration: none;">.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For <del style="font-weight: bold; text-decoration: none;">more details </del>please see [[Machine learning force field: Theory#Regression|here]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>For <ins style="font-weight: bold; text-decoration: none;">the theory of the available methods </ins>please see [[Machine learning force field: Theory#Regression|here]].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following options are available to solve for <math>\mathbf{w}</math>:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following options are available to solve for <math>\mathbf{w}</math>:</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20541&oldid=prev
Karsai at 15:47, 3 July 2023
2023-07-03T15:47:55Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:47, 3 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Line 11:</td>
<td colspan="2" class="diff-lineno">Line 11:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For more details please see [[Machine learning force field: Theory#<del style="font-weight: bold; text-decoration: none;">Matrix vector form of linear equations</del>|here]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>For more details please see [[Machine learning force field: Theory#<ins style="font-weight: bold; text-decoration: none;">Regression</ins>|here]].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following options are available to solve for <math>\mathbf{w}</math>:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The following options are available to solve for <math>\mathbf{w}</math>:</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20020&oldid=prev
Karsai at 14:15, 31 March 2023
2023-03-31T14:15:14Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:15, 31 March 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l27">Line 27:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>However, {{TAG|ML_IALGO_LINREG}}=4 needs significantly more memory than {{TAG|ML_IALGO_LINREG}}=1 (at least twice that much). Please always monitor the memory estimates in {{TAG|ML_LOGFILE}}! It should be also noted that {{TAG|ML_IALGO_LINREG}}=4 is computationally somewhat more demanding than {{TAG|ML_IALGO_LINREG}}=1, but it typically requires between a few minutes and an hour. So usually the extra cost is negligible compared to the original training.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>However, {{TAG|ML_IALGO_LINREG}}=4 needs significantly more memory than {{TAG|ML_IALGO_LINREG}}=1 (at least twice that much). Please always monitor the memory estimates in <ins style="font-weight: bold; text-decoration: none;">the </ins>{{TAG|ML_LOGFILE}}! It should be also noted that {{TAG|ML_IALGO_LINREG}}=4 is computationally somewhat more demanding than {{TAG|ML_IALGO_LINREG}}=1, but it typically requires between a few minutes and an hour. So usually the extra cost is negligible compared to the original training.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related tags and articles ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related tags and articles ==</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20019&oldid=prev
Karsai at 14:13, 31 March 2023
2023-03-31T14:13:24Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:13, 31 March 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24">Line 24:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). {{TAG|ML_MODE}}= ''REFIT'' employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">From </del>{{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;">For </ins>{{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{TAG|ML_IALGO_LINREG}}=4 dramatically improves the condition number of the fitting compared to {{TAG|ML_IALGO_LINREG}}=1 since it directly uses the design matrix. In contrast {{TAG|ML_IALGO_LINREG}}=1 requires to use the covariance matrix (square of the design matrix), which effectively doubles the condition number.</div></td></tr>
</table>
Karsai
https://vasp.at/wiki/index.php?title=ML_IALGO_LINREG&diff=20018&oldid=prev
Karsai at 14:12, 31 March 2023
2023-03-31T14:12:46Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:12, 31 March 2023</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Refitting''':</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Refitting''':</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). <del style="font-weight: bold; text-decoration: none;">This mode </del>employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>Although the above modes result in an {{TAG|ML_FFN}} file that could be used for production runs, we strongly advise to refit the {{TAG|ML_ABN}} files. For that copy the {{TAG|ML_ABN}} file to the {{TAG|ML_AB}} file and use {{TAG|ML_MODE}}= ''REFIT'' (if Bayesian error estimation is required during production runs {{TAG|ML_MODE}}= ''REFITBAYESIAN'' is an option, but at the cost of significatnly slower calculation time). <ins style="font-weight: bold; text-decoration: none;">{{TAG|ML_MODE}}= ''REFIT'' </ins>employs {{TAG|ML_IALGO_LINREG}}=4 by default.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>From {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>From {{TAG|ML_IALGO_LINREG}}>1, {{TAG|ML_IALGO_LINREG}}=3 and 4 are the most tested approaches and we use {{TAG|ML_IALGO_LINREG}}=4 routinely before employing a machine learned force field. {{TAG|ML_IALGO_LINREG}}=4 gives more stable force fields and better fitting accuracy than {{TAG|ML_IALGO_LINREG}}=3, due to the regularization term employed. </div></td></tr>
</table>
Karsai