Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Alborzpour, Jonathan P [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2016 |
|---|
| Rechteinformationen: |
Nutzungsrecht: © Author(s) |
|---|
| Übergeordnetes Werk: |
Enthalten in: The journal of chemical physics - Melville, NY : AIP, 1933, 145(2016), 17 |
|---|---|
| Übergeordnetes Werk: |
volume:145 ; year:2016 ; number:17 |
| Links: |
|---|
| DOI / URN: |
10.1063/1.4964902 |
|---|
| Katalog-ID: |
OLC1984591053 |
|---|
| LEADER | 01000caa a2200265 4500 | ||
|---|---|---|---|
| 001 | OLC1984591053 | ||
| 003 | DE-627 | ||
| 005 | 20230714224235.0 | ||
| 007 | tu | ||
| 008 | 161202s2016 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1063/1.4964902 |2 doi | |
| 028 | 5 | 2 | |a PQ20161201 |
| 035 | |a (DE-627)OLC1984591053 | ||
| 035 | |a (DE-599)GBVOLC1984591053 | ||
| 035 | |a (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 | ||
| 035 | |a (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 540 |a 530 |q DE-600 |
| 100 | 1 | |a Alborzpour, Jonathan P |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| 264 | 1 | |c 2016 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 520 | |a Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. | ||
| 540 | |a Nutzungsrecht: © Author(s) | ||
| 700 | 1 | |a Tew, David P |4 oth | |
| 700 | 1 | |a Habershon, Scott |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |t The journal of chemical physics |d Melville, NY : AIP, 1933 |g 145(2016), 17 |w (DE-627)129079049 |w (DE-600)3113-6 |w (DE-576)014411660 |x 0021-9606 |7 nnns |
| 773 | 1 | 8 | |g volume:145 |g year:2016 |g number:17 |
| 856 | 4 | 1 | |u http://dx.doi.org/10.1063/1.4964902 |3 Volltext |
| 856 | 4 | 2 | |u http://dx.doi.org/10.1063/1.4964902 |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-PHY | ||
| 912 | |a SSG-OLC-CHE | ||
| 912 | |a SSG-OLC-PHA | ||
| 912 | |a SSG-OLC-DE-84 | ||
| 912 | |a GBV_ILN_21 | ||
| 912 | |a GBV_ILN_59 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_2016 | ||
| 912 | |a GBV_ILN_2279 | ||
| 951 | |a AR | ||
| 952 | |d 145 |j 2016 |e 17 | ||
| author_variant |
j p a jp jpa |
|---|---|
| matchkey_str |
article:00219606:2016----::fiinadcuaevlainfoetaeegmtieeetfrunudnmcu |
| hierarchy_sort_str |
2016 |
| publishDate |
2016 |
| allfields |
10.1063/1.4964902 doi PQ20161201 (DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat DE-627 ger DE-627 rakwb eng 540 530 DE-600 Alborzpour, Jonathan P verfasserin aut Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. Nutzungsrecht: © Author(s) Tew, David P oth Habershon, Scott oth Enthalten in The journal of chemical physics Melville, NY : AIP, 1933 145(2016), 17 (DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 0021-9606 nnns volume:145 year:2016 number:17 http://dx.doi.org/10.1063/1.4964902 Volltext http://dx.doi.org/10.1063/1.4964902 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 AR 145 2016 17 |
| spelling |
10.1063/1.4964902 doi PQ20161201 (DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat DE-627 ger DE-627 rakwb eng 540 530 DE-600 Alborzpour, Jonathan P verfasserin aut Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. Nutzungsrecht: © Author(s) Tew, David P oth Habershon, Scott oth Enthalten in The journal of chemical physics Melville, NY : AIP, 1933 145(2016), 17 (DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 0021-9606 nnns volume:145 year:2016 number:17 http://dx.doi.org/10.1063/1.4964902 Volltext http://dx.doi.org/10.1063/1.4964902 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 AR 145 2016 17 |
| allfields_unstemmed |
10.1063/1.4964902 doi PQ20161201 (DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat DE-627 ger DE-627 rakwb eng 540 530 DE-600 Alborzpour, Jonathan P verfasserin aut Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. Nutzungsrecht: © Author(s) Tew, David P oth Habershon, Scott oth Enthalten in The journal of chemical physics Melville, NY : AIP, 1933 145(2016), 17 (DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 0021-9606 nnns volume:145 year:2016 number:17 http://dx.doi.org/10.1063/1.4964902 Volltext http://dx.doi.org/10.1063/1.4964902 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 AR 145 2016 17 |
| allfieldsGer |
10.1063/1.4964902 doi PQ20161201 (DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat DE-627 ger DE-627 rakwb eng 540 530 DE-600 Alborzpour, Jonathan P verfasserin aut Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. Nutzungsrecht: © Author(s) Tew, David P oth Habershon, Scott oth Enthalten in The journal of chemical physics Melville, NY : AIP, 1933 145(2016), 17 (DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 0021-9606 nnns volume:145 year:2016 number:17 http://dx.doi.org/10.1063/1.4964902 Volltext http://dx.doi.org/10.1063/1.4964902 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 AR 145 2016 17 |
| allfieldsSound |
10.1063/1.4964902 doi PQ20161201 (DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat DE-627 ger DE-627 rakwb eng 540 530 DE-600 Alborzpour, Jonathan P verfasserin aut Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. Nutzungsrecht: © Author(s) Tew, David P oth Habershon, Scott oth Enthalten in The journal of chemical physics Melville, NY : AIP, 1933 145(2016), 17 (DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 0021-9606 nnns volume:145 year:2016 number:17 http://dx.doi.org/10.1063/1.4964902 Volltext http://dx.doi.org/10.1063/1.4964902 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 AR 145 2016 17 |
| language |
English |
| source |
Enthalten in The journal of chemical physics 145(2016), 17 volume:145 year:2016 number:17 |
| sourceStr |
Enthalten in The journal of chemical physics 145(2016), 17 volume:145 year:2016 number:17 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| dewey-raw |
540 |
| isfreeaccess_bool |
false |
| container_title |
The journal of chemical physics |
| authorswithroles_txt_mv |
Alborzpour, Jonathan P @@aut@@ Tew, David P @@oth@@ Habershon, Scott @@oth@@ |
| publishDateDaySort_date |
2016-01-01T00:00:00Z |
| hierarchy_top_id |
129079049 |
| dewey-sort |
3540 |
| id |
OLC1984591053 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1984591053</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230714224235.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">161202s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1063/1.4964902</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20161201</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1984591053</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1984591053</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">540</subfield><subfield code="a">530</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Alborzpour, Jonathan P</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Author(s)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tew, David P</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Habershon, Scott</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of chemical physics</subfield><subfield code="d">Melville, NY : AIP, 1933</subfield><subfield code="g">145(2016), 17</subfield><subfield code="w">(DE-627)129079049</subfield><subfield code="w">(DE-600)3113-6</subfield><subfield code="w">(DE-576)014411660</subfield><subfield code="x">0021-9606</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:145</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:17</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1063/1.4964902</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">http://dx.doi.org/10.1063/1.4964902</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-CHE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-DE-84</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_21</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_59</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2016</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2279</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">145</subfield><subfield code="j">2016</subfield><subfield code="e">17</subfield></datafield></record></collection>
|
| author |
Alborzpour, Jonathan P |
| spellingShingle |
Alborzpour, Jonathan P ddc 540 Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| authorStr |
Alborzpour, Jonathan P |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129079049 |
| format |
Article |
| dewey-ones |
540 - Chemistry & allied sciences 530 - Physics |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0021-9606 |
| topic_title |
540 530 DE-600 Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| topic |
ddc 540 |
| topic_unstemmed |
ddc 540 |
| topic_browse |
ddc 540 |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| author2_variant |
d p t dp dpt s h sh |
| hierarchy_parent_title |
The journal of chemical physics |
| hierarchy_parent_id |
129079049 |
| dewey-tens |
540 - Chemistry 530 - Physics |
| hierarchy_top_title |
The journal of chemical physics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129079049 (DE-600)3113-6 (DE-576)014411660 |
| title |
Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| ctrlnum |
(DE-627)OLC1984591053 (DE-599)GBVOLC1984591053 (PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0 (KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat |
| title_full |
Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| author_sort |
Alborzpour, Jonathan P |
| journal |
The journal of chemical physics |
| journalStr |
The journal of chemical physics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2016 |
| contenttype_str_mv |
txt |
| author_browse |
Alborzpour, Jonathan P |
| container_volume |
145 |
| class |
540 530 DE-600 |
| format_se |
Aufsätze |
| author-letter |
Alborzpour, Jonathan P |
| doi_str_mv |
10.1063/1.4964902 |
| dewey-full |
540 530 |
| title_sort |
efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using gaussian process regression |
| title_auth |
Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| abstract |
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. |
| abstractGer |
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. |
| abstract_unstemmed |
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OLC-DE-84 GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2016 GBV_ILN_2279 |
| container_issue |
17 |
| title_short |
Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression |
| url |
http://dx.doi.org/10.1063/1.4964902 |
| remote_bool |
false |
| author2 |
Tew, David P Habershon, Scott |
| author2Str |
Tew, David P Habershon, Scott |
| ppnlink |
129079049 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth oth |
| doi_str |
10.1063/1.4964902 |
| up_date |
2024-07-04T00:57:18.132Z |
| _version_ |
1803608012234948608 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1984591053</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230714224235.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">161202s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1063/1.4964902</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20161201</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1984591053</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1984591053</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c692-cc8dab03c6fffc3418e834ab688eeea90a2a60b8e8cc3ea74b3467e383697a2e0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0048355920160000145001700000efficientandaccurateevaluationofpotentialenergymat</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">540</subfield><subfield code="a">530</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Alborzpour, Jonathan P</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Author(s)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tew, David P</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Habershon, Scott</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of chemical physics</subfield><subfield code="d">Melville, NY : AIP, 1933</subfield><subfield code="g">145(2016), 17</subfield><subfield code="w">(DE-627)129079049</subfield><subfield code="w">(DE-600)3113-6</subfield><subfield code="w">(DE-576)014411660</subfield><subfield code="x">0021-9606</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:145</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:17</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1063/1.4964902</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">http://dx.doi.org/10.1063/1.4964902</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-CHE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-DE-84</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_21</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_59</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2016</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2279</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">145</subfield><subfield code="j">2016</subfield><subfield code="e">17</subfield></datafield></record></collection>
|
| score |
7.400467 |