"This tutorial shows how to find descriptive parameters (short formulas) that predict the crystal structure (here, rocksalt (RS), zincblende (ZB) or CsCl), using the example of octet binary compounds. It is based on the algorithm Sure Independent Screening followed by l0 minimization (SIS+l0), that enables to search for optimal descriptor by scanning huge feature spaces.",
"This tutorial shows how to find descriptive parameters (short formulas) that predict the crystal structure (here, rocksalt (RS), zincblende (ZB) or CsCl), using the example of octet binary compounds. It is based on the algorithm Sure Independent Screening followed by l0 minimization (SIS+l0), that enables to search for optimal descriptor by scanning huge feature spaces.",
...
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"<span style=\"font-weight: bold;\">Idea: </span> Starting from simple physical quantities (\"building blocks\", here properties of the constituent free atoms such as orbital radii), millions (or billions) of candidate formulas are generated by applying arithmetic operations combining building blocks, for example forming sums and products of them. These candidate formulas constitute the so-called \"feature space\". Then a feature selection method (SIS+l0) is used to select only a few of these formulas that explain the data.",
"<span style=\"font-weight: bold;\">Idea: </span> Starting from simple physical quantities (\"building blocks\", here properties of the constituent free atoms such as orbital radii), millions (or billions) of candidate formulas are generated by applying arithmetic operations combining building blocks, for example forming sums and products of them. These candidate formulas constitute the so-called \"feature space\". Then a feature selection method (SIS+l0) is used to select only a few of these formulas that explain the data.",
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"object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<label style=\"text-align: left; color: #20335d; font-weight: 900; font-size: 18pt; padding-top: 2em;\">\n Predicting energy differences between different crystal structures II: huge feature space</label><br><label style=\"color: #20335d;font-weight: 900; font-size: 15pt;\"> (Meta-)stability of octet-binary compounds</label>\n <p></p>\n <p style=\"font-size: 15px;\">Emre Ahmetcik, Angelo Ziletti, Runhai Ouyang, Ankit Kariryaa, Fawzi Mohamed, Luca Ghiringhelli, Matthias Scheffler [version 2017-01-25]<span style=\"font-size: smaller;\">[version 2017-01-25]</span></p>\n \n<div style=\"padding-top: 1em;\">\nThis tutorial shows how to find descriptive parameters (short formulas) that predict the crystal structure (here, rocksalt (RS), zincblende (ZB) or CsCl), using the example of octet binary compounds. It is based on the algorithm Sure Independent Screening followed by l0 minimization (SIS+l0), that enables to search for optimal descriptor by scanning huge feature spaces.\n <div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nR. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.\n</div>\nWith the default settings, the method reproduces the same results from:\n<div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nL. M. Ghiringhelli, J. Vybiral, S. V. Levchenko, C. Draxl, M. Scheffler: <span style=\"font-style: italic;\">Big Data of Materials Science: Critical Role of the Descriptor</span>, Phys. Rev. Lett. 114, 105503 (2015) <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\">[PDF]</a>,\n</div>\nthat were obtained obtained by applying the <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">[LASSO+l0 algorithm]</a>. Click on <b>Run</b> below to reproduce results from this publication; click <b>Background</b> for an explanation of the approach; or, modify <b>Settings</b> to produce your own results.\n</div>\n<div style=\"padding-top: 2ex;\">\n<span style=\"font-weight: bold;\">Idea: </span> Starting from simple physical quantities (\"building blocks\", here properties of the constituent free atoms such as orbital radii), millions (or billions) of candidate formulas are generated by applying arithmetic operations combining building blocks, for example forming sums and products of them. These candidate formulas constitute the so-called \"feature space\". Then a feature selection method (SIS+l0) is used to select only a few of these formulas that explain the data.\n</div>"
"object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<label style=\"text-align: left; color: #20335d; font-weight: 900; font-size: 18pt; padding-top: 2em;\">\n Predicting energy differences between crystal structures</label><br><label style=\"color: #20335d;font-weight: 900; font-size: 15pt;\"> (Meta-)stability of octet-binary compounds</label>\n <p></p>\n <p style=\"font-size: 15px;\">Angelo Ziletti, Emre Ahmetcik, Runhai Ouyang, Ankit Kariryaa, Fawzi Mohamed, Luca Ghiringhelli, Matthias Scheffler [version 2017-01-25]<span style=\"font-size: smaller;\">[version 2017-02-02]</span></p>\n \n<div style=\"padding-top: 1em;\">\nThis tutorial shows how to find descriptive parameters (short formulas) that predict the crystal structure (here, rocksalt (RS), zincblende (ZB) or CsCl), using the example of octet binary compounds. It is based on the algorithm Sure Independent Screening followed by l0 minimization (SIS+l0), that enables to search for optimal descriptor by scanning huge feature spaces.\n <div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nR. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.\n</div>\nWith the default settings, the method reproduces the same results from:\n<div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nL. M. Ghiringhelli, J. Vybiral, S. V. Levchenko, C. Draxl, M. Scheffler: <span style=\"font-style: italic;\">Big Data of Materials Science: Critical Role of the Descriptor</span>, Phys. Rev. Lett. 114, 105503 (2015) <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\">[PDF]</a>,\n</div>\nthat were obtained obtained by applying the <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">[LASSO+l0 algorithm]</a>. Click on <b>Run</b> below to reproduce results from this publication; click <b>Background</b> for an explanation of the approach; or, modify <b>Settings</b> to produce your own results.\n</div>\n<div style=\"padding-top: 2ex;\">\n<span style=\"font-weight: bold;\">Idea: </span> Starting from simple physical quantities (\"building blocks\", here properties of the constituent free atoms such as orbital radii), millions (or billions) of candidate formulas are generated by applying arithmetic operations combining building blocks, for example forming sums and products of them. These candidate formulas constitute the so-called \"feature space\". Then a feature selection method (SIS+l0) is used to select only a few of these formulas that explain the data.\n</div>"
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"During the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: ",
"During the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: ",
" <ul>",
" <ul>",
" <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>",
" <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>",
"<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the first twodimensions.</li>",
"<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the two-dimensional descriptor.</li>",
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"<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>",
"<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>",
" </div>",
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...
@@ -256,7 +257,7 @@
...
@@ -256,7 +257,7 @@
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"object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<script>\nvar run_lasso = function() {\n $(\"#lasso_result_button\").removeClass(\"active\").addClass(\"disabled\");\n getFeatures();\n getOperators();\n beaker.max_dim = $(\"#lasso_max_dim_selector\").val();\n beaker.structures_diff = $(\"#lasso_structures_diff\").val();\n beaker.n_comb = $(\"#n_comb\").val();\n beaker.n_sis = $(\"#n_sis\").val();\n beaker.units = $(\"#units_select\").val();\n beaker.evaluate(\"calc_cell\"); // evaluate cells with tag \"lasso_cell\"\n // view_result()\n};\nvar reset_lasso = function(){\n beaker.evaluate(\"lasso-settings-cell\");\n var e = document.getElementById('lasso-hidden-settings-div');\n var b = document.getElementById('lasso-hidden-settings-button');\n e.style.display = 'block';\n b.style.display = 'inline';\n};\nvar getFeatures = function() {\n beaker.selected_feature_list = [];\n $('#lasso_features_select input:checkbox').each(function () {\n if(this.checked )\n beaker.selected_feature_list.push(this.value);\n });\n};\nvar getOperators = function() {\n beaker.allowed_operations = [];\n $('#lasso_operators_select input:checkbox').each(function () {\n if(this.checked )\n beaker.allowed_operations.push(this.value);\n });\n}; \n\nvar toggle_settings = function(){\n var e = document.getElementById('lasso-hidden-settings-div');\n var b = document.getElementById('lasso-hidden-settings-button');\n if(e.style.display == 'block'){\n e.style.display = 'none';\n b.style.display = 'none';\n }\n else{\n e.style.display = 'block';\n b.style.display = 'inline';\n }\n};\nbeaker.view_result = function(result_link) {\n// beaker.evaluate(\"lasso_viewer_result\").then(function(x) {\n $(\"#lasso_result_button\").attr(\"href\", result_link);\n// }); \n $(\"#lasso_result_button\").removeClass(\"disabled\").addClass(\"active\");\n}\n\n\n\n\n\n\n\n</script>\n<style type=\"text/css\">\n .lasso_instructions{\n font-size: 15px;\n } \n</style>\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-motivation-modal\">\n Background\n</button> \n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-motivation-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-motivation-modal-label\">\n <div class=\"modal-dialog modal-lg\" role=\"document\">\n <div class=\"modal-content\">\n <div class=\"modal-header\">\n <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n <h4 class=\"modal-title\" id=\"lasso-motivation-modal-label\">Background</h4>\n </div>\n <div class=\"modal-body lasso_instructions\">\n <p>We present a tool for predicting the crystal structure of octet binary compounds, by using a set of descriptive parameters (a descriptor) based on free-atom data of the atomic species constituting the binary material. This task is similar to the one presented in the tutorial <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">\"[Predicting energy differences between different crystal structures I: large feature space]\"</a>\". In contrast to that tutorial, here we apply a newly developed method: Sure Independent Screening - Sparse Approximation (SIS-SA), that allows to find an optimal descriptor in a huge feature space containing billions of features.\nThe method is described in:\n</p><div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nR. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.\n</div>\n<p></p>\n \n<p>SIS-SA works iteratively. In the first iteration, a number k of features is collected as those that have the largest correlation (scalar product) with the property vector. The feature with the largest correlation is simply the 1D descriptor. Next, a residual is constructed as the error made at the first iteration. A new set of k features is now selected as those having the largest correlation with the residual. The 2D descriptor is the pair of features that yield the smallest fitting error upon least square regression, among all possible pairs contained in the union of the sets selected in this and the first iteration. In each next iteration a new residual is constructed as the error made in the previous iteration, then a new set of k features is extracted as those that have largest correlation with each new residual. The nD descriptor is the n-tuple of features that yield the smallest fitting error upon least square regression, among all possible n-tuples contained in the union of the sets obtained in each new iteration and all the previous iterations. If k=1 the method collapses to the so-called orthogonal matching pursuit.\n</p>\n\n <p>The prediction of the ground-state structure for binary compounds from a simple descriptor has a notable history in materials science [1-7], where descriptors were designed by chemically/physically-inspired intuition. The tool presented here allows for the machine-learning-aided automatic discovery of a descriptor and a model for the prediction of the difference in energy between a selected pair of structures for 82 octet binary materials.</p>\n\n\n <p> By running the tutorial with the default setting, the (RS vs. ZB) results of the <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\" target=\"_blank\">PRL 2015</a> identified by the LASSO+L0 method can be recovered.</p>\n \n\n <p>References:</p>\n <ol>\n <li>J. A. van Vechten, Phys. Rev. 182, 891 (1969).</li>\n <li>J. C. Phillips, Rev. Mod. Phys. 42, 317 (1970).</li>\n <li>J. St. John and A.N. Bloch, Phys. Rev. Lett. 33, 1095 (1974).</li>\n <li>J. R. Chelikowsky and J. C. Phillips, Phys. Rev. B 17, 2453 (1978).</li>\n <li>A. Zunger, Phys. Rev. B 22, 5839 (1980).</li>\n <li>D. G. Pettifor, Solid State Commun. 51, 31 (1984).</li>\n <li>Y. Saad, D. Gao, T. Ngo, S. Bobbitt, J. R. Chelikowsky, and W. Andreoni, Phys. Rev. B 85, 104104 (2012).</li>\n </ol>\n </div>\n <div class=\"modal-footer\">\n <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!-- <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n </div>\n </div>\n </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-instructions-modal\">\n Instructions\n</button> \n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-instructions-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-instructions-modal-label\">\n <div class=\"modal-dialog\" role=\"document\">\n <div class=\"modal-content\">\n <div class=\"modal-header\">\n <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n <h4 class=\"modal-title\" id=\"lasso-instructions-modal-label\">Instructions</h4>\n </div>\n <div class=\"modal-body lasso_instructions\">\n<p>In this example, you can run a compressed-sensing based algorithm for finding the optimal descriptor and model that predicts the difference in energy between crystal structures (here, rocksalt vs. zincblende vs. CsCl structure). </p>\n\n<p>The descriptor is selected out of a large number of candidates constructed as functions of basic input features, the primary features. </p>\n\n<p>By clicking <b>Settings</b> you can select the structure pair of interest (either RS/ZB or CsCl/ZB), the primary features as well as which kind of unary and binary operations are allowed from the checklist below. Moreover the dimension of the output energies (kcal/mol or eV) and the following three parameters of the SIS+L0 algorithm can be specified: \n </p><ul>\n <li>Number of iterations for the construction for the feature space: How often the selected operations are applied to build the feature space. At each step the opreations are applied on all features created untill the current step. </li>\n <li>Optimal descriptor maximum dimension: Number of SIS+SA iterations.</li>\n <li>Number of collected features per SIS iteration.</li>\n </ul> \n \n<p></p>\n \n \n<p> After the preferred settings have been adjusted, click <b>RUN</b> for performing the calculations (loading the values of the primary features, creation of the feature space, and optimization via SIS+L0). </p>\n\nDuring the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: \n <ul>\n <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>\n<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the first twodimensions.</li>\n</ul>\n<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>\n </div>\n <div class=\"modal-footer\">\n <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!-- <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n </div>\n </div>\n </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" onclick=\"toggle_settings()\">\n Settings\n</button> \n\n<a target=\"_blank\" href=\"http://forum.analytics-toolkit.nomad-coe.eu/\" class=\"btn btn-primary\"> Tell us what you think</a>\n\n"
"object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<script>\nvar run_lasso = function() {\n $(\"#lasso_result_button\").removeClass(\"active\").addClass(\"disabled\");\n getFeatures();\n getOperators();\n beaker.max_dim = $(\"#lasso_max_dim_selector\").val();\n beaker.structures_diff = $(\"#lasso_structures_diff\").val();\n beaker.n_comb = $(\"#n_comb\").val();\n beaker.n_sis = $(\"#n_sis\").val();\n beaker.units = $(\"#units_select\").val();\n beaker.evaluate(\"calc_cell\"); // evaluate cells with tag \"lasso_cell\"\n // view_result()\n};\nvar reset_lasso = function(){\n beaker.evaluate(\"lasso-settings-cell\");\n var e = document.getElementById('lasso-hidden-settings-div');\n var b = document.getElementById('lasso-hidden-settings-button');\n e.style.display = 'block';\n b.style.display = 'inline';\n};\nvar getFeatures = function() {\n beaker.selected_feature_list = [];\n $('#lasso_features_select input:checkbox').each(function () {\n if(this.checked )\n beaker.selected_feature_list.push(this.value);\n });\n};\nvar getOperators = function() {\n beaker.allowed_operations = [];\n $('#lasso_operators_select input:checkbox').each(function () {\n if(this.checked )\n beaker.allowed_operations.push(this.value);\n });\n}; \n\nvar toggle_settings = function(){\n var e = document.getElementById('lasso-hidden-settings-div');\n var b = document.getElementById('lasso-hidden-settings-button');\n if(e.style.display == 'block'){\n e.style.display = 'none';\n b.style.display = 'none';\n }\n else{\n e.style.display = 'block';\n b.style.display = 'inline';\n }\n};\nbeaker.view_result = function(result_link) {\n// beaker.evaluate(\"lasso_viewer_result\").then(function(x) {\n $(\"#lasso_result_button\").attr(\"href\", result_link);\n// }); \n $(\"#lasso_result_button\").removeClass(\"disabled\").addClass(\"active\");\n}\n\n\n\n\n\n\n\n</script>\n<style type=\"text/css\">\n .lasso_instructions{\n font-size: 15px;\n } \n</style>\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-motivation-modal\">\n Background\n</button> \n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-motivation-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-motivation-modal-label\">\n <div class=\"modal-dialog modal-lg\" role=\"document\">\n <div class=\"modal-content\">\n <div class=\"modal-header\">\n <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n <h4 class=\"modal-title\" id=\"lasso-motivation-modal-label\">Background</h4>\n </div>\n <div class=\"modal-body lasso_instructions\">\n <p>We present a tool for predicting the crystal structure of octet binary compounds, by using a set of descriptive parameters (a descriptor) based on free-atom data of the atomic species constituting the binary material. This task is similar to the one presented in the tutorial <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">\"[Predicting energy differences between different crystal structures I: large feature space]\"</a>\". In contrast to that tutorial, here we apply a newly developed method: Sure Independent Screening - Sparse Approximation (SIS-SA), that allows to find an optimal descriptor in a huge feature space containing billions of features.\nThe method is described in:\n</p><div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nR. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.\n</div>\n<p></p>\n \n<p>SIS-SA works iteratively. In the first iteration, a number k of features is collected as those that have the largest correlation (scalar product) with the property vector. The feature with the largest correlation is simply the 1D descriptor. Next, a residual is constructed as the error made at the first iteration. A new set of k features is now selected as those having the largest correlation with the residual. The 2D descriptor is the pair of features that yield the smallest fitting error upon least square regression, among all possible pairs contained in the union of the sets selected in this and the first iteration. In each next iteration a new residual is constructed as the error made in the previous iteration, then a new set of k features is extracted as those that have largest correlation with each new residual. The nD descriptor is the n-tuple of features that yield the smallest fitting error upon least square regression, among all possible n-tuples contained in the union of the sets obtained in each new iteration and all the previous iterations. If k=1 the method collapses to the so-called orthogonal matching pursuit.\n</p>\n\n <p>The prediction of the ground-state structure for binary compounds from a simple descriptor has a notable history in materials science [1-7], where descriptors were designed by chemically/physically-inspired intuition. The tool presented here allows for the machine-learning-aided automatic discovery of a descriptor and a model for the prediction of the difference in energy between a selected pair of structures for 82 octet binary materials.</p>\n\n\n <p> By running the tutorial with the default setting, the (RS vs. ZB) results of the <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\" target=\"_blank\">PRL 2015</a> identified by the LASSO+L0 method can be recovered.</p>\n \n\n <p>References:</p>\n <ol>\n <li>J. A. van Vechten, Phys. Rev. 182, 891 (1969).</li>\n <li>J. C. Phillips, Rev. Mod. Phys. 42, 317 (1970).</li>\n <li>J. St. John and A.N. Bloch, Phys. Rev. Lett. 33, 1095 (1974).</li>\n <li>J. R. Chelikowsky and J. C. Phillips, Phys. Rev. B 17, 2453 (1978).</li>\n <li>A. Zunger, Phys. Rev. B 22, 5839 (1980).</li>\n <li>D. G. Pettifor, Solid State Commun. 51, 31 (1984).</li>\n <li>Y. Saad, D. Gao, T. Ngo, S. Bobbitt, J. R. Chelikowsky, and W. Andreoni, Phys. Rev. B 85, 104104 (2012).</li>\n </ol>\n </div>\n <div class=\"modal-footer\">\n <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!-- <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n </div>\n </div>\n </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-instructions-modal\">\n Instructions\n</button> \n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-instructions-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-instructions-modal-label\" style=\"display: none;\">\n <div class=\"modal-dialog\" role=\"document\">\n <div class=\"modal-content\">\n <div class=\"modal-header\">\n <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n <h4 class=\"modal-title\" id=\"lasso-instructions-modal-label\">Instructions</h4>\n </div>\n <div class=\"modal-body lasso_instructions\">\n<p>In this example, you can run a compressed-sensing based algorithm for finding the optimal descriptor and model that predicts the difference in energy between crystal structures (here, rocksalt vs. zincblende vs. CsCl structure). </p>\n\n<p>The descriptor is selected out of a large number of candidates constructed as functions of basic input features, the primary features. </p>\n\n<p>By clicking <b>Settings</b> you can select the structure pair of interest (either RS/ZB or CsCl/ZB), the primary features as well as which kind of unary and binary operations are allowed from the checklist below. Moreover the dimension of the output energies (kcal/mol or eV) and the following three parameters of the SIS+L0 algorithm can be specified: \n </p><ul>\n <li>Number of iterations for the construction for the feature space: How often the selected operations are applied to build the feature space. At each step the opreations are applied on all features created untill the current step. </li>\n <li>Optimal descriptor maximum dimension: Number of SIS+SA iterations.</li>\n <li>Number of collected features per SIS iteration.</li>\n </ul> \n \n<p></p>\n \n \n<p> After the preferred settings have been adjusted, click <b>RUN</b> for performing the calculations (loading the values of the primary features, creation of the feature space, and optimization via SIS+L0). </p>\n\nDuring the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: \n <ul>\n <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>\n<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the two-dimensional descriptor.</li>\n</ul>\n<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>\n </div>\n <div class=\"modal-footer\">\n <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!-- <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n </div>\n </div>\n </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" onclick=\"toggle_settings()\">\n Settings\n</button> \n\n<a target=\"_blank\" href=\"http://forum.analytics-toolkit.nomad-coe.eu/\" class=\"btn btn-primary\"> Tell us what you think</a>\n\n"
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"dimensions of the optimized descriptor will be opened\"> ",
"dimensions of the optimized descriptor will be opened\"> ",
