ML RCUT2 - Revision history

Kresse: Type corrected.

2023-05-09T13:35:23Z

Type corrected.

← Older revision		Revision as of 13:35, 9 May 2023
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	\rho_{ij}\left(\mathbf{r}\right) = f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right)		\rho_{ij}\left(\mathbf{r}\right) = f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right)
	</math>		</math>

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.		and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.
	{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory ~~accuraof the descriptor cy~~ '''and''' speed.}}		{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuracy '''and''' speed.}}

	For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> ~~might~~ improve the accuracy,		For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> can improve the accuracy,

	== Related tags and articles ==		== Related tags and articles ==

Kresse at 12:08, 9 May 2023

2023-05-09T12:08:12Z

← Older revision		Revision as of 12:08, 9 May 2023
Line 12:		Line 12:

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.		and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.
	{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve ~~satisfying accuracy~~ '''and''' speed.}}		{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuraof the descriptor cy '''and''' speed.}}

	For materials ~~(i.e. organic molecules, polymers)~~ containing only H, B, C, O, N, and F, the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> might improve the accuracy,		For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> might improve the accuracy,

	== Related tags and articles ==		== Related tags and articles ==

Kresse at 12:06, 9 May 2023

2023-05-09T12:06:11Z

← Older revision		Revision as of 12:06, 9 May 2023
Line 12:		Line 12:

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.		and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.
	{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost ~~of the descriptor~~ as the cutoff sphere contains more neighbor atoms. A good compromise is ~~always~~ system-dependent, therefore different values should be tested to achieve satisfying accuracy '''and''' speed.}}		{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfying accuracy '''and''' speed.}}

	For materials (i.e. organic molecules, polymers) containing only H, B, C, O, N, and F, the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> might improve the accuracy,		For materials (i.e. organic molecules, polymers) containing only H, B, C, O, N, and F, the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> might improve the accuracy,

Kresse: Hints on how to vary ML_RCUT1

2023-05-09T12:04:26Z

Hints on how to vary ML_RCUT1

← Older revision		Revision as of 12:04, 9 May 2023
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	{{TAGDEF\|ML_RCUT2\|[real]\|5.0}}		{{TAGDEF\|ML_RCUT2\|[real]\|5.0}}

	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method.		Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method. The unit of the cut-off radius is <math>\AA</math>.
	----		----
	The angular descriptor is constructed from		The angular descriptor is constructed from
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	{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent, therefore different values should be tested to achieve satisfying accuracy '''and''' speed.}}		{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent, therefore different values should be tested to achieve satisfying accuracy '''and''' speed.}}

	~~The unit of~~ the ~~cut-off radius~~ is <math>\AA</math>.		For materials (i.e. organic molecules, polymers) containing only H, B, C, O, N, and F, the learning efficiency might increase when ML_RCUT2 is set to values around 4 <math>\AA</math> (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 <math>\AA</math> might improve the accuracy,

	== Related tags and articles ==		== Related tags and articles ==

Karsai at 11:55, 31 March 2023

2023-03-31T11:55:25Z

← Older revision		Revision as of 11:55, 31 March 2023
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	{{DISPLAYTITLE:ML_RCUT2}}		{{DISPLAYTITLE:ML_RCUT2}}
	{{TAGDEF\|ML_RCUT2\|[real]\|~~{{TAG\|ML_RCUT1}}~~}}		{{TAGDEF\|ML_RCUT2\|[real]\|5.0}}

	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method.		Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method.

Karsai: /* Related tags and articles */

2022-04-08T13:30:32Z

Karsai at 07:39, 7 April 2022

2022-04-07T07:39:16Z

← Older revision		Revision as of 07:39, 7 April 2022
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			{{DISPLAYTITLE:ML_RCUT2}}
	{{TAGDEF\|ML_RCUT2\|[real]\|{{TAG\|ML_RCUT1}}}}		{{TAGDEF\|ML_RCUT2\|[real]\|{{TAG\|ML_RCUT1}}}}

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	The unit of the cut-off radius is <math>\AA</math>.		The unit of the cut-off radius is <math>\AA</math>.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT1}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_MRB2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT1}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_MRB2}}

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	----		----

	[[Category:INCAR]][[Category:Machine Learning]][[Category:Machine Learned Force Fields~~]][[Category: Alpha~~]]		[[Category:INCAR tag]][[Category:Machine Learning]][[Category:Machine Learned Force Fields]]

Kresse: /* Related Tags and Sections */

2021-11-05T07:32:15Z

Related Tags and Sections

← Older revision		Revision as of 07:32, 5 November 2021
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	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT1}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT1}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_MRB2}}

Singraber at 10:09, 13 October 2021

2021-10-13T10:09:46Z

← Older revision		Revision as of 10:09, 13 October 2021
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	{{TAGDEF\|ML_RCUT2\|[real]\|ML_RCUT1}}		{{TAGDEF\|ML_RCUT2\|[real]\|{{TAG\|ML_RCUT1}}}}

	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method ~~as described in [[Machine learning force field: Theory#Descriptors\|this section]]~~.		Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method.
	----		----
			The angular descriptor is constructed from

			<math>
			\rho_{i}^{(3)}\left(r,s,\theta\right) = \iint d\hat{\mathbf{r}} d\hat{\mathbf{s}} \delta\left(\hat{\mathbf{r}}\cdot\hat{\mathbf{s}} - \mathrm{cos}\theta\right) \sum\limits_{j=1}^{N_{a}} \sum\limits_{k \ne j}^{N_{a}} \rho_{ik} \left(r\hat{\mathbf{r}}\right) \rho_{ij} \left(s\hat{\mathbf{s}}\right), \quad \text{where} \quad
			\rho_{ij}\left(\mathbf{r}\right) = f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right)
			</math>

			and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(3)}_i(r)</math> yields the expansion coefficients <math>p_{n\nu l}^{i}</math> which are used in practice to describe the atomic environment (see [[Machine learning force field: Theory#Descriptors\|this section]] for details). The tag {{TAG\|ML_RCUT2}} sets the cutoff radius <math>R_\text{cut}</math> at which the cutoff function <math>f_{\mathrm{cut}}\left(r_{ij}\right)</math> decays to zero.
			{{NB\|mind\|The cutoff radius determines how many neighbor atoms <math>N_\mathrm{a}</math> are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent, therefore different values should be tested to achieve satisfying accuracy '''and''' speed.}}

	The unit of the cut-off radius is <math>\AA</math>.		The unit of the cut-off radius is <math>\AA</math>.

Singraber at 20:56, 10 October 2021

2021-10-10T20:56:04Z

← Older revision		Revision as of 20:56, 10 October 2021
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	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors\|this section]].		Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the angular descriptor <math>\rho^{(3)}_i(r)</math> in the machine learning force field method as described in [[Machine learning force field: Theory#Descriptors\|this section]].
	----		----
	The unit of the cut-off radius is ~~given in~~ <math>\AA</math>.		The unit of the cut-off radius is <math>\AA</math>.

	== Related Tags and Sections ==		== Related Tags and Sections ==

← Older revision		Revision as of 13:30, 8 April 2022
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	----		----

	[[Category:INCAR tag]][[Category:Machine ~~Learning]][[Category:Machine Learned Force Fields~~]]		[[Category:INCAR tag]][[Category:Machine-learned force fields]]