ML LCOUPLE: Difference between revisions
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{{TAGDEF| | {{DISPLAYTITLE:ML_LCOUPLE}} | ||
{{TAGDEF|ML_LCOUPLE|[logical]|.FALSE.}} | |||
Description: This tag specifies whether | Description: This tag specifies whether thermodynamic integration is activated in order to calculate the chemical potentials within the machine learning force field method. | ||
---- | ---- | ||
In thermodynamic integration a coupling parameter <math>\lambda</math> is introduced to the Hamiltonian to smoothly switch between a "non-interacting" reference state and a "fully-interacting" state. The change of the free energy along this path is written as | |||
{{sc| | <math> | ||
\Delta \mu = \int\limits_{0}^{1} \langle \frac{dH(\lambda)}{d\lambda} \rangle_{\lambda} d\lambda. | |||
</math> | |||
Using machine learning force fields the Hamiltonian can be written as | |||
<math> | |||
H (\lambda) = \sum\limits_{i=1}^{N_{a}} \frac{|\mathbf{p}_{i}|^2}{2m_{i}} + \sum\limits_{i \notin M} U_{i}(\lambda) + \lambda \sum\limits_{i \in M} U_{i}(\lambda) + \sum\limits_{i}^{N_{a}} U_{i,\mathbf{atom}}. | |||
</math> | |||
where <math>N_{a}</math> denotes the number of atoms and <math> U_{i,\mathbf{atom}}</math> is an atomic reference energy for a single non interacting atom. The first term in the equation describes the potential energy and the second and third term describe the potential energy of an atom <math>i</math>. The index <math>M</math> denotes the atoms whose interaction is controlled by a coupling parameter. The interactions of the atoms are controlled by scaling the contributions to the atom density via the coupling parameter | |||
<math> | |||
\rho (\mathbf{r},\lambda) = \sum\limits_{j\notin M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right] + \lambda \sum\limits_{j\in M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right]. | |||
</math> | |||
Further details on the implementation can be found in reference {{cite|jinnouchiti:prb:2020}}. | |||
For thermodynamic integration the following parameters have to be set: | |||
*{{TAGO|ML_MODE|run}}. | |||
*{{TAGO|ML_LCOUPLE|.TRUE.}}. | |||
*The number of atoms for which a coupling parameter is introduced (<math>i \in M </math>): {{TAG|ML_NATOM_COUPLED}}. | |||
*The list of atom indices that for that the coupling parameter is applied in the interaction: {{TAG|ML_ICOUPLE}}. | |||
*The strength of the coupling parameter <math>\lambda</math> between 0 and 1: {{TAG|ML_RCOUPLE}}. | |||
The derivative of the hamiltonian with respect to the coupling constant <math>dH/d\lambda</math> is written out at every MD step to the {{TAG|ML_LOGFILE}}. A sample output should look like this: | |||
# DCOUPLE ################################ | |||
# DCOUPLE This line shows the derivative of the Hamiltonian with respect to coupling constant (dH/dlambda). | |||
# DCOUPLE | |||
# DCOUPLE nstep .......... MD time step or input structure counter | |||
# DCOUPLE der_H_lambda ... dH/dlambda | |||
# DCOUPLE ################################ | |||
# DCOUPLE nstep der_H_lambda | |||
# DCOUPLE 2 3 | |||
# DCOUPLE ################################ | |||
DCOUPLE 1 -1.08332135E+01 | |||
DCOUPLE 2 -1.08132321E+01 | |||
DCOUPLE 3 -1.07631992E+01 | |||
DCOUPLE 4 -1.06786675E+01 | |||
DCOUPLE 5 -1.05493088E+01 | |||
DCOUPLE 6 -1.03561161E+01 | |||
DCOUPLE 7 -1.00762443E+01 | |||
DCOUPLE 8 -9.69961878E+00 | |||
DCOUPLE 9 -9.25531640E+00 | |||
DCOUPLE 10 -8.82525354E+00 | |||
... | |||
== References == | |||
<references/> | |||
<noinclude> | |||
== Related tags and articles == | |||
{{TAG|ML_LMLFF}}, {{TAG|ML_NATOM_COUPLED}}, {{TAG|ML_ICOUPLE}}, {{TAG|ML_RCOUPLE}} | |||
{{sc|ML_LCOUPLE|Examples|Examples that use this tag}} | |||
---- | ---- | ||
[[Category:INCAR]][[Category:Machine | [[Category:INCAR tag]][[Category:Machine-learned force fields]] |
Latest revision as of 11:07, 11 November 2023
ML_LCOUPLE = [logical]
Default: ML_LCOUPLE = .FALSE.
Description: This tag specifies whether thermodynamic integration is activated in order to calculate the chemical potentials within the machine learning force field method.
In thermodynamic integration a coupling parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \lambda } is introduced to the Hamiltonian to smoothly switch between a "non-interacting" reference state and a "fully-interacting" state. The change of the free energy along this path is written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \Delta \mu = \int\limits_{0}^{1} \langle \frac{dH(\lambda)}{d\lambda} \rangle_{\lambda} d\lambda. }
Using machine learning force fields the Hamiltonian can be written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle H (\lambda) = \sum\limits_{i=1}^{N_{a}} \frac{|\mathbf{p}_{i}|^2}{2m_{i}} + \sum\limits_{i \notin M} U_{i}(\lambda) + \lambda \sum\limits_{i \in M} U_{i}(\lambda) + \sum\limits_{i}^{N_{a}} U_{i,\mathbf{atom}}. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N_{{a}} denotes the number of atoms and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle U_{i,\mathbf{atom}}} is an atomic reference energy for a single non interacting atom. The first term in the equation describes the potential energy and the second and third term describe the potential energy of an atom Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): i . The index Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): M denotes the atoms whose interaction is controlled by a coupling parameter. The interactions of the atoms are controlled by scaling the contributions to the atom density via the coupling parameter
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \rho (\mathbf{r},\lambda) = \sum\limits_{j\notin M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right] + \lambda \sum\limits_{j\in M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right]. }
Further details on the implementation can be found in reference [1].
For thermodynamic integration the following parameters have to be set:
ML_MODE = run
.ML_LCOUPLE = .TRUE.
.- The number of atoms for which a coupling parameter is introduced (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle i \in M } ): ML_NATOM_COUPLED.
- The list of atom indices that for that the coupling parameter is applied in the interaction: ML_ICOUPLE.
- The strength of the coupling parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \lambda } between 0 and 1: ML_RCOUPLE.
The derivative of the hamiltonian with respect to the coupling constant Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle dH/d\lambda} is written out at every MD step to the ML_LOGFILE. A sample output should look like this:
# DCOUPLE ################################ # DCOUPLE This line shows the derivative of the Hamiltonian with respect to coupling constant (dH/dlambda). # DCOUPLE # DCOUPLE nstep .......... MD time step or input structure counter # DCOUPLE der_H_lambda ... dH/dlambda # DCOUPLE ################################ # DCOUPLE nstep der_H_lambda # DCOUPLE 2 3 # DCOUPLE ################################ DCOUPLE 1 -1.08332135E+01 DCOUPLE 2 -1.08132321E+01 DCOUPLE 3 -1.07631992E+01 DCOUPLE 4 -1.06786675E+01 DCOUPLE 5 -1.05493088E+01 DCOUPLE 6 -1.03561161E+01 DCOUPLE 7 -1.00762443E+01 DCOUPLE 8 -9.69961878E+00 DCOUPLE 9 -9.25531640E+00 DCOUPLE 10 -8.82525354E+00 ...
References
Related tags and articles
ML_LMLFF, ML_NATOM_COUPLED, ML_ICOUPLE, ML_RCOUPLE