ML RCUT1 - Revision history

Huebsch at 06:34, 11 May 2023

2023-05-11T06:34:47Z

← Older revision		Revision as of 06:34, 11 May 2023
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	</math>		</math>

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{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_RCUT1}} 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^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{i}</math>, which are used in practice to describe the atomic environment; refer to the [[Machine learning force field: Theory#Descriptors\|theory of machine-learned force fields]] for details. The tag {{TAG\|ML_RCUT1}} 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 considered to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is too small. 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 considered to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is too small. 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.}}

Huebsch at 06:13, 11 May 2023

2023-05-11T06:13:47Z

← Older revision		Revision as of 06:13, 11 May 2023
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	{{TAGDEF\|ML_RCUT1\|[real]\|8.0}}		{{TAGDEF\|ML_RCUT1\|[real]\|8.0}}

	Description: ~~This flag sets~~ the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_i(r)</math> in ~~the machine learning force field method~~.		Description: Sets the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_i(r)</math> in <math>\AA</math>.
	----		----
	The radial descriptor is constructed from		The radial descriptor for machine-learned force fields is constructed from

	<math>		<math>
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	</math>		</math>

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{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_RCUT1}} 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^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{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_RCUT1}} 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 considered to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is too small. 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>.

Karsai at 08:05, 9 May 2023

2023-05-09T08:05:36Z

← Older revision		Revision as of 08:05, 9 May 2023
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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>.
	~~The value of {{TAG\|ML_RCUT1}} is the default value for {{TAG\|ML_RCUT2}}.~~

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

Karsai at 11:55, 31 March 2023

2023-03-31T11:55:00Z

← Older revision		Revision as of 11:55, 31 March 2023
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	{{DISPLAYTITLE:ML_RCUT1}}		{{DISPLAYTITLE:ML_RCUT1}}
	{{TAGDEF\|ML_RCUT1\|[real]\|5.0}}		{{TAGDEF\|ML_RCUT1\|[real]\|8.0}}

	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_i(r)</math> in the machine learning force field method.		Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_i(r)</math> in the machine learning force field method.

Karsai: /* Related tags and articles */

2022-04-08T13:30:24Z

Karsai at 07:38, 7 April 2022

2022-04-07T07:38:50Z

← Older revision		Revision as of 07:38, 7 April 2022
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			{{DISPLAYTITLE:ML_RCUT1}}
	{{TAGDEF\|ML_RCUT1\|[real]\|5.0}}		{{TAGDEF\|ML_RCUT1\|[real]\|5.0}}

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	The value of {{TAG\|ML_RCUT1}} is the default value for {{TAG\|ML_RCUT2}}.		The value of {{TAG\|ML_RCUT1}} is the default value for {{TAG\|ML_RCUT2}}.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_MRB2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT2}}, {{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 */

2021-11-05T07:32:01Z

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_RCUT2}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}m {{TAG\|ML_MRB2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}, {{TAG\|ML_MRB2}}

	{{sc\|ML_RCUT1\|Examples\|Examples that use this tag}}		{{sc\|ML_RCUT1\|Examples\|Examples that use this tag}}

Kresse: /* Related Tags and Sections */

2021-11-05T07:31:49Z

Related Tags and Sections

← Older revision		Revision as of 07:31, 5 November 2021
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	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}		{{TAG\|ML_LMLFF}}, {{TAG\|ML_RCUT2}}, {{TAG\|ML_W1}}, {{TAG\|ML_SION1}}, {{TAG\|ML_SION2}}, {{TAG\|ML_MRB1}}m {{TAG\|ML_MRB2}}

	{{sc\|ML_RCUT1\|Examples\|Examples that use this tag}}		{{sc\|ML_RCUT1\|Examples\|Examples that use this tag}}

Singraber at 12:10, 13 October 2021

2021-10-13T12:10:53Z

← Older revision		Revision as of 12:10, 13 October 2021
Line 10:		Line 10:
	</math>		</math>

	and <math>g\left(\mathbf{r}\right)</math> is an approximation of the delta function. A basis set expansion of <math>\rho^{(2)}_i(r)</math> yields the expansion coefficients <math>~~c_n~~^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_RCUT1}} 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^{(2)}_i(r)</math> yields the expansion coefficients <math>c_{n00}^{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_RCUT1}} 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 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.}}

Singraber at 10:02, 13 October 2021

2021-10-13T10:02:13Z

← Older revision		Revision as of 10:02, 13 October 2021
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	{{TAGDEF\|ML_RCUT1\|[real]\|5.0}}		{{TAGDEF\|ML_RCUT1\|[real]\|5.0}}

	Description: This flag sets the cutoff radius <math>R_\text{cut}</math> for the radial descriptor <math>\rho^{(2)}_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 radial descriptor <math>\rho^{(2)}_i(r)</math> in the machine learning force field method.
	----		----
			The radial descriptor is constructed from

			<math>
			\rho_{i}^{(2)}\left(r\right) = \frac{1}{4\pi} \int \rho_{i}\left(r\hat{\mathbf{r}}\right) d\hat{\mathbf{r}}, \quad \text{where} \quad
			\rho_{i}\left(\mathbf{r}\right) = \sum\limits_{j=1}^{N_{\mathrm{a}}} 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^{(2)}_i(r)</math> yields the expansion coefficients <math>c_n^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_RCUT1}} 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>.
	The value of {{TAG\|ML_RCUT1}} is the default value for {{TAG\|ML_RCUT2}}.		The value of {{TAG\|ML_RCUT1}} is the default value for {{TAG\|ML_RCUT2}}.

← 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]]