ML EPS REG - Revision history

https://vasp.at/wiki/index.php?action=history&feed=atom&title=ML_EPS_REG ML EPS REG - Revision history 2026-04-15T17:37:33Z Revision history for this page on the wiki MediaWiki 1.43.8 https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=17769&oldid=prev Karsai at 08:48, 16 May 2022 2022-05-16T08:48:15Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 08:48, 16 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are included in the above equations, whereas smaller eigenvalues are disregarded (they are anyway potentially inaccurate because of loss of significance).</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are included in the above equations, whereas smaller eigenvalues are disregarded (they are anyway potentially inaccurate because of loss of significance).</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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></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;">The smaller the value of {{TAG|ML_EPS_REG}}, the smaller the error of the fit can potentially become. But at the same time, the danger of over fitting increases. We determined empirically that the default of {{TAG|ML_EPS_REG}}=1E-14 is fairly safe. If a user desires higher accuracy, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 (lower values are not recommended), but the user should very carefully monitor the convergence of the calculations as described below. </del></div></td><td colspan="2" class="diff-side-added"></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>If at any point during iterating the above equations, the quadratic norm of errors (eight column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) becomes too large (more than 1.2 times larger than in previous iterations), the code assumes that numerical issues</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>If at any point during iterating the above equations, the quadratic norm of errors (eight column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) becomes too large (more than 1.2 times larger than in previous iterations), the code assumes that numerical issues</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=17768&oldid=prev Karsai at 08:47, 16 May 2022 2022-05-16T08:47:49Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 08:47, 16 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</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>{{DISPLAYTITLE:ML_EPS_REG}}</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>{{DISPLAYTITLE:ML_EPS_REG}}</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>{{TAGDEF|ML_EPS_REG|[real]|1E-<del style="font-weight: bold; text-decoration: none;">14</del>}}</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_EPS_REG|[real]|1E-<ins style="font-weight: bold; text-decoration: none;">15</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>Description: Initial value for the threshold of the eigenvalues of the covariance matrix in the evidence approximation.</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: Initial value for the threshold of the eigenvalues of the covariance matrix in the evidence approximation.</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=16605&oldid=prev Karsai: /* Related tags and articles */ 2022-04-08T13:22:26Z

<p><span class="autocomment">Related tags and articles</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 13:22, 8 April 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l34">Line 34:</td> <td colspan="2" class="diff-lineno">Line 34:</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>----</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>----</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>[[Category:INCAR tag]][[Category:Machine <del style="font-weight: bold; text-decoration: none;">Learning]][[Category:Machine Learned Force Fields</del>]]</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>[[Category:INCAR tag]][[Category:Machine<ins style="font-weight: bold; text-decoration: none;">-learned force fields</ins>]]</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=15670&oldid=prev Karsai at 07:23, 7 April 2022 2022-04-07T07:23:35Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 07:23, 7 April 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2" class="diff-side-deleted"></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;">{{DISPLAYTITLE:ML_EPS_REG}}</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>{{TAGDEF|ML_EPS_REG|[real]|1E-14}}</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>{{TAGDEF|ML_EPS_REG|[real]|1E-14}}</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 colspan="2" class="diff-lineno" id="mw-diff-left-l26">Line 26:</td> <td colspan="2" class="diff-lineno">Line 27:</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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), this is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), this is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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>== Related <del style="font-weight: bold; text-decoration: none;">Tags </del>and <del style="font-weight: bold; text-decoration: none;">Sections </del>==</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>== Related <ins style="font-weight: bold; text-decoration: none;">tags </ins>and <ins style="font-weight: bold; text-decoration: none;">articles </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>{{TAG|ML_LMLFF}}, {{TAG|ML_IALGO_LINREG}}, {{TAG|ML_IREG}}, {{TAG|ML_SIGV0}}, {{TAG|ML_SIGW0}}</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_LMLFF}}, {{TAG|ML_IALGO_LINREG}}, {{TAG|ML_IREG}}, {{TAG|ML_SIGV0}}, {{TAG|ML_SIGW0}}</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 colspan="2" class="diff-lineno" id="mw-diff-left-l33">Line 33:</td> <td colspan="2" class="diff-lineno">Line 34:</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>----</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>----</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>[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields<del style="font-weight: bold; text-decoration: none;">]][[Category: Alpha</del>]]</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>[[Category:INCAR <ins style="font-weight: bold; text-decoration: none;">tag</ins>]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]]</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=14815&oldid=prev Kresse: Wording further improved 2022-03-23T17:22:40Z

<p>Wording further improved</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 17:22, 23 March 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">Line 17:</td> <td colspan="2" class="diff-lineno">Line 17:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are included in the above equations, whereas <del style="font-weight: bold; text-decoration: none;">the other </del>eigenvalues are disregarded.</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are included in the above equations, whereas <ins style="font-weight: bold; text-decoration: none;">smaller </ins>eigenvalues are disregarded <ins style="font-weight: bold; text-decoration: none;">(they are anyway potentially inaccurate because of loss of significance)</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" 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>The smaller the value of {{TAG|ML_EPS_REG}}, the smaller the error of the fit can potentially become. But at the same time, the danger of over fitting <del style="font-weight: bold; text-decoration: none;">potentially </del>increases. We determined empirically that the default of {{TAG|ML_EPS_REG}}=1E-14 is fairly safe. If a user desires higher accuracy <del style="font-weight: bold; text-decoration: none;">of the force field</del>, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 (lower values are not recommended), but the user should very carefully monitor the convergence of the calculations as described below. </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>The smaller the value of {{TAG|ML_EPS_REG}}, the smaller the error of the fit can potentially become. But at the same time, the danger of over fitting increases. We determined empirically that the default of {{TAG|ML_EPS_REG}}=1E-14 is fairly safe. If a user desires higher accuracy, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 (lower values are not recommended), but the user should very carefully monitor the convergence of the calculations as described below. </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>If at any point during iterating, <del style="font-weight: bold; text-decoration: none;">the approximation of the square of </del>the quadratic norm of errors (eight column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) becomes too large (more than 1.2 times larger than in previous iterations), then {{TAG|ML_EPS_REG}} is automatically doubled. <del style="font-weight: bold; text-decoration: none;">Whenever </del>the regression <del style="font-weight: bold; text-decoration: none;">doesn't </del>converge within 10 steps, {{TAG|ML_EPS_REG}} is increased by a factor of 4<del style="font-weight: bold; text-decoration: none;">. This counter is also reset whenever {{TAG|ML_EPS_REG}} is changed</del>. The maximum allowed iteration depths is 50 (the iteration number is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]]). When <del style="font-weight: bold; text-decoration: none;">this value is </del>reached, no force field is created and there is most likely something seriously wrong in the calculation.</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>If at any point during iterating <ins style="font-weight: bold; text-decoration: none;">the above equations</ins>, the quadratic norm of errors (eight column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) becomes too large (more than 1.2 times larger than in previous iterations), <ins style="font-weight: bold; text-decoration: none;">the code assumes that numerical issues</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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;">(loss of significance) have occurred, and </ins>then {{TAG|ML_EPS_REG}} is automatically doubled. <ins style="font-weight: bold; text-decoration: none;">Furthermore, if </ins>the regression <ins style="font-weight: bold; text-decoration: none;">does not </ins>converge within 10 steps, {{TAG|ML_EPS_REG}} is <ins style="font-weight: bold; text-decoration: none;">also </ins>increased by a factor of 4. The maximum allowed iteration depths is 50 (the iteration number is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]]). When <ins style="font-weight: bold; text-decoration: none;">50 iterations are </ins>reached, no force field is created and there is most likely something seriously wrong in the calculation.</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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), this is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), this is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </div></td></tr> </table>

Kresse https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=14814&oldid=prev Kresse: Wording improved 2022-03-23T17:17:34Z

<p>Wording improved</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 17:17, 23 March 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">Line 17:</td> <td colspan="2" class="diff-lineno">Line 17:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are <del style="font-weight: bold; text-decoration: none;">contributing by </del>the above equations.</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are <ins style="font-weight: bold; text-decoration: none;">included in </ins>the above equations<ins style="font-weight: bold; text-decoration: none;">, whereas the other eigenvalues are disregarded</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" 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>The smaller the value of {{TAG|ML_EPS_REG}} the smaller the error of the fit. But at the same time the <del style="font-weight: bold; text-decoration: none;">effects </del>of over fitting <del style="font-weight: bold; text-decoration: none;">increase</del>. We determined empirically that the default of {{TAG|ML_EPS_REG}}=1E-14 is safe <del style="font-weight: bold; text-decoration: none;">in most cases</del>. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 <del style="font-weight: bold; text-decoration: none;">or </del>lower, but the user should very carefully monitor the convergence of the calculations as described below. </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>The smaller the value of {{TAG|ML_EPS_REG}}<ins style="font-weight: bold; text-decoration: none;">, </ins>the smaller the error of the fit <ins style="font-weight: bold; text-decoration: none;">can potentially become</ins>. But at the same time<ins style="font-weight: bold; text-decoration: none;">, </ins>the <ins style="font-weight: bold; text-decoration: none;">danger </ins>of over fitting <ins style="font-weight: bold; text-decoration: none;">potentially increases</ins>. We determined empirically that the default of {{TAG|ML_EPS_REG}}=1E-14 is <ins style="font-weight: bold; text-decoration: none;">fairly </ins>safe. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 <ins style="font-weight: bold; text-decoration: none;">(</ins>lower <ins style="font-weight: bold; text-decoration: none;">values are not recommended)</ins>, but the user should very carefully monitor the convergence of the calculations as described below. </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>If at any point <del style="font-weight: bold; text-decoration: none;">in the iterations of </del>the <del style="font-weight: bold; text-decoration: none;">Evidence Approximation </del>of the square of the quadratic norm of errors (<del style="font-weight: bold; text-decoration: none;">eigth </del>column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) <del style="font-weight: bold; text-decoration: none;">gets </del>too <del style="font-weight: bold; text-decoration: none;">big </del>(more than 1.2 times larger than <del style="font-weight: bold; text-decoration: none;">before</del>) then {{TAG|ML_EPS_REG}} is doubled. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. <del style="font-weight: bold; text-decoration: none;">The </del>counter <del style="font-weight: bold; text-decoration: none;">for the 10 strucures </del>is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration <del style="font-weight: bold; text-decoration: none;">steps are </del>50 (the number <del style="font-weight: bold; text-decoration: none;">of each step </del>is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]])<del style="font-weight: bold; text-decoration: none;">, but when </del>this value is reached no force field is created and there is most likely something seriously wrong in the calculation.</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>If at any point <ins style="font-weight: bold; text-decoration: none;">during iterating, </ins>the <ins style="font-weight: bold; text-decoration: none;">approximation </ins>of the square of the quadratic norm of errors (<ins style="font-weight: bold; text-decoration: none;">eight </ins>column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) <ins style="font-weight: bold; text-decoration: none;">becomes </ins>too <ins style="font-weight: bold; text-decoration: none;">large </ins>(more than 1.2 times larger than <ins style="font-weight: bold; text-decoration: none;">in previous iterations</ins>)<ins style="font-weight: bold; text-decoration: none;">, </ins>then {{TAG|ML_EPS_REG}} is <ins style="font-weight: bold; text-decoration: none;">automatically </ins>doubled. Whenever the regression doesn't converge within 10 steps<ins style="font-weight: bold; text-decoration: none;">, </ins>{{TAG|ML_EPS_REG}} is increased by a factor of 4. <ins style="font-weight: bold; text-decoration: none;">This </ins>counter <ins style="font-weight: bold; text-decoration: none;"> </ins>is <ins style="font-weight: bold; text-decoration: none;">also </ins>reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration <ins style="font-weight: bold; text-decoration: none;">depths is </ins>50 (the <ins style="font-weight: bold; text-decoration: none;">iteration </ins>number is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]])<ins style="font-weight: bold; text-decoration: none;">. When </ins>this value is reached<ins style="font-weight: bold; text-decoration: none;">, </ins>no force field is created and there is most likely something seriously wrong in the calculation.</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>The seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), <del style="font-weight: bold; text-decoration: none;">it </del>is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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>The seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), <ins style="font-weight: bold; text-decoration: none;">this </ins>is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 Sections ==</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 Sections ==</div></td></tr> </table>

Kresse https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=13736&oldid=prev Karsai at 11:02, 11 January 2022 2022-01-11T11:02:53Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 11:02, 11 January 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24">Line 24:</td> <td colspan="2" class="diff-lineno">Line 24:</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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></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 Sections ==</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 Sections ==</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=13735&oldid=prev Karsai at 11:01, 11 January 2022 2022-01-11T11:01:43Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 11:01, 11 January 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>The smaller the value of {{TAG|ML_EPS_REG}} the smaller the error of the fit. But at the same time the effects of over fitting increase. We determined empirically that the default of {{TAG|ML_EPS_REG}}1E-14 is safe in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the convergence of the calculations as described below. </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>The smaller the value of {{TAG|ML_EPS_REG}} the smaller the error of the fit. But at the same time the effects of over fitting increase. We determined empirically that the default of {{TAG|ML_EPS_REG}}<ins style="font-weight: bold; text-decoration: none;">=</ins>1E-14 is safe in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the convergence of the calculations as described below. </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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. The counter for the 10 strucures is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration steps are 50 (the number of each step is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]]), but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation.</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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. The counter for the 10 strucures is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration steps are 50 (the number of each step is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]]), but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation.</div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=13734&oldid=prev Karsai at 10:59, 11 January 2022 2022-01-11T10:59:55Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 10:59, 11 January 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>The smaller the value of {{TAG|ML_EPS_REG}} <del style="font-weight: bold; text-decoration: none;">the </del>the smaller the error of the fit. But at the same time the effects of <del style="font-weight: bold; text-decoration: none;">overfitting </del>increase. We determined empirically that the default <del style="font-weight: bold; text-decoration: none;">value </del>of 1E-14 is <del style="font-weight: bold; text-decoration: none;">a </del>safe <del style="font-weight: bold; text-decoration: none;">value </del>in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the convergence of the calculations as described below. </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>The smaller the value of {{TAG|ML_EPS_REG}} the smaller the error of the fit. But at the same time the effects of <ins style="font-weight: bold; text-decoration: none;">over fitting </ins>increase. We determined empirically that the default of <ins style="font-weight: bold; text-decoration: none;">{{TAG|ML_EPS_REG}}</ins>1E-14 is safe in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the convergence of the calculations as described below. </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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. The counter for the 10 strucures is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration steps are 50, but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation.</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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. The counter for the 10 strucures is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration steps are 50 <ins style="font-weight: bold; text-decoration: none;">(the number of each step is the second entry of <code>REGR/REGRF</code> in [[ML_LOGFILE]])</ins>, but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation.</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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </div></td></tr> </table>

Karsai https://vasp.at/wiki/index.php?title=ML_EPS_REG&diff=13733&oldid=prev Karsai at 10:55, 11 January 2022 2022-01-11T10:55:20Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 10:55, 11 January 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>All eigenvalues satisfying <math>\lambda_{i} / \lambda_{\mathrm{max}} </math> > {{TAG|ML_EPS_REG}} are contributing by the above equations.</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>The smaller the value of {{TAG|ML_EPS_REG}} the the smaller the error of the fit. But at the same time the effects of overfitting increase. We determined empirically that the default value of 1E-14 is a safe value in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the <del style="font-weight: bold; text-decoration: none;">calculation </del>as described below. </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>The smaller the value of {{TAG|ML_EPS_REG}} the the smaller the error of the fit. But at the same time the effects of overfitting increase. We determined empirically that the default value of 1E-14 is a safe value in most cases. If a user desires higher accuracy of the force field, the user can try to set {{TAG|ML_EPS_REG}}=1E-15 or lower, but the user should very carefully monitor the <ins style="font-weight: bold; text-decoration: none;">convergence of the calculations </ins>as described below. </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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled. </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>If at any point in the iterations of the Evidence Approximation of the square of the quadratic norm of errors (eigth column of <code>REGR/REGRF</code> in [[ML_LOGFILE]]) gets too big (more than 1.2 times larger than before) then {{TAG|ML_EPS_REG}} is doubled<ins style="font-weight: bold; text-decoration: none;">. Whenever the regression doesn't converge within 10 steps {{TAG|ML_EPS_REG}} is increased by a factor of 4. The counter for the 10 strucures is reset whenever {{TAG|ML_EPS_REG}} is changed. The maximum allowed iteration steps are 50, but when this value is reached no force field is created and there is most likely something seriously wrong in the calculation</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>The seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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 seventh entry of <code>REGR/REGRF</code> in the [[ML_LOGFILE]] shows the ratio of the regularization (<math>\sigma_{v}^{2}/ \sigma_{w}^{2}</math>) and the largest eigenvalue. Usually this number is a number with many varying digits. If this number becomes a "well rounded" number (e.g. 1.00000000E-14), it is an indication that the cap for the current {{TAG|ML_EPS_REG}} is reached. That means that regularization becomes crucial. </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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></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;"></del></div></td><td colspan="2" class="diff-side-added"></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;"></del></div></td><td colspan="2" class="diff-side-added"></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;"> </del></div></td><td colspan="2" class="diff-side-added"></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;"><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> </table>

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