Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. A...
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Veröffentlicht in: | The Journal of chemical physics 2023-06, Vol.158 (21) |
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creator | Van Benschoten, William Z. Weiler, Laura Smith, Gabriel J. Man, Songhang DeMello, Taylor Shepherd, James J. |
description | We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy. |
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National Energy Research Scientific Computing Center (NERSC)</creatorcontrib><description>We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/5.0150702</identifier><identifier>PMID: 37265216</identifier><identifier>CODEN: JCPSA6</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>Configuration interaction ; Density ; Entropy ; finite electronic temperature ; free energy calculations ; full configuration interaction ; Gaussian process ; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY ; Machine learning ; Numerical integration ; Regression models ; Specific heat ; thermodynamic properties</subject><ispartof>The Journal of chemical physics, 2023-06, Vol.158 (21)</ispartof><rights>Author(s)</rights><rights>2023 Author(s). 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National Energy Research Scientific Computing Center (NERSC)</creatorcontrib><title>Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data</title><title>The Journal of chemical physics</title><addtitle>J Chem Phys</addtitle><description>We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.</description><subject>Configuration interaction</subject><subject>Density</subject><subject>Entropy</subject><subject>finite electronic temperature</subject><subject>free energy calculations</subject><subject>full configuration interaction</subject><subject>Gaussian process</subject><subject>INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY</subject><subject>Machine learning</subject><subject>Numerical integration</subject><subject>Regression models</subject><subject>Specific heat</subject><subject>thermodynamic properties</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp90c2KFDEQAOAgijuuHnwBCXpRodf8dDrdRxnWVVjxoueQTiqzWbqT3iQtzrP4smaYcQUFT5WCj6pUFULPKbmgpOPvxAWhgkjCHqANJf3QyG4gD9GGEEaboSPdGXqS8y0hhErWPkZnXLJOMNpt0M_LCUxJMXiD8wLGu_q4AV2w0Ys2vnjIWAeLIVS1HDKX4owthOzLHs-6JP8D3606lHXGn2MogLc6TRGv2YcdvtJrzl4HvKRoIGecYJdq9DHgErHztfYuaetrg4yjwyH6vMdWF_0UPXJ6yvDsFM_Rtw-XX7cfm-svV5-2768b07aiNEK7kXd2dL1upW0JyFHAwCm0mg1Q876zwzhy4GMr5GCpEYwwJ4AKapk1_By9PNaNuXiV69BgbkwMoW5G0WHgnNKKXh9RneNuhVzU7LOBadIB4poV6xnjkg9SVvrqL3ob1xTqCAdVT8Ao66t6c1QmxZwTOLUkP-u0V5Sow1mVUKezVvviVHEdZ7D38vcdK3h7BIff61KXe2--x_Snklqs-x_-t_Uv6Qa7Cg</recordid><startdate>20230607</startdate><enddate>20230607</enddate><creator>Van Benschoten, William Z.</creator><creator>Weiler, Laura</creator><creator>Smith, Gabriel J.</creator><creator>Man, Songhang</creator><creator>DeMello, Taylor</creator><creator>Shepherd, James J.</creator><general>American Institute of Physics</general><general>American Institute of Physics (AIP)</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><scope>OIOZB</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0002-7983-5558</orcidid><orcidid>https://orcid.org/0000-0002-6164-485X</orcidid><orcidid>https://orcid.org/000000026164485X</orcidid><orcidid>https://orcid.org/0000000279835558</orcidid></search><sort><creationdate>20230607</creationdate><title>Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data</title><author>Van Benschoten, William Z. ; Weiler, Laura ; Smith, Gabriel J. ; Man, Songhang ; DeMello, Taylor ; Shepherd, James J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c445t-5afb36dbf8a47d40e7b5e931e4a29e40e86d9bb3e3b4579d1c5202f5e151d2dc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Configuration interaction</topic><topic>Density</topic><topic>Entropy</topic><topic>finite electronic temperature</topic><topic>free energy calculations</topic><topic>full configuration interaction</topic><topic>Gaussian process</topic><topic>INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY</topic><topic>Machine learning</topic><topic>Numerical integration</topic><topic>Regression models</topic><topic>Specific heat</topic><topic>thermodynamic properties</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Van Benschoten, William Z.</creatorcontrib><creatorcontrib>Weiler, Laura</creatorcontrib><creatorcontrib>Smith, Gabriel J.</creatorcontrib><creatorcontrib>Man, Songhang</creatorcontrib><creatorcontrib>DeMello, Taylor</creatorcontrib><creatorcontrib>Shepherd, James J.</creatorcontrib><creatorcontrib>Univ. of Iowa, Iowa City, IA (United States)</creatorcontrib><creatorcontrib>Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV - Hybrid</collection><collection>OSTI.GOV</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Van Benschoten, William Z.</au><au>Weiler, Laura</au><au>Smith, Gabriel J.</au><au>Man, Songhang</au><au>DeMello, Taylor</au><au>Shepherd, James J.</au><aucorp>Univ. of Iowa, Iowa City, IA (United States)</aucorp><aucorp>Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data</atitle><jtitle>The Journal of chemical physics</jtitle><addtitle>J Chem Phys</addtitle><date>2023-06-07</date><risdate>2023</risdate><volume>158</volume><issue>21</issue><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>37265216</pmid><doi>10.1063/5.0150702</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-7983-5558</orcidid><orcidid>https://orcid.org/0000-0002-6164-485X</orcidid><orcidid>https://orcid.org/000000026164485X</orcidid><orcidid>https://orcid.org/0000000279835558</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Configuration interaction Density Entropy finite electronic temperature free energy calculations full configuration interaction Gaussian process INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY Machine learning Numerical integration Regression models Specific heat thermodynamic properties |
title | Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data |
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