added resources from theses/master-thesis

cosmo/dirac-rep.tex

+%%%%%%%%%%%%%%%%%%%  dirac-rep.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Macros to be used top simplify typesetting the Dirac notation for ML
+% representations introduced in
+% Willatt, Musil, Ceriotti, J. Chem. Phys. 150 (2019) DOI: 10.1063/1.5090481
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Main macros are \rep and \field that can be used to typeset a bra-ket
+% notation for a representation, and the symmetrized-fields notation for
+% n-body features.
+% Usage:
+% \rep<X|   ->    bra containing X
+% \rep|A>   ->    ket containing A
+% \rep<X||A>   -> bra-ket <X|A>
+%
+% \field{\rho}_i^{\nu}   ->  a \rho_i^{\otimes \nu} indicating a (\nu+1)-body
+%                            \rho-based representation centred on atom i
+% \field{\rho}_i[V]_i   -> \rho_i\otimes V_i indicating a mix of \rho and V
+%                             based, i-centred representations
+% \field[\lambda\mu]{\rho}_i^2   ->  \lambda-SOAP representation
+%
+% Furthermore, this contains a number of shortcuts for the density expansion
+% coefficients, e.g. \enlk generates a n l k, while a subscript notation
+% attaches an index to each item, e.g. \nlm_1 generates n_1 l_1 m_1
+
+% include guards
+\ifdefined\DIRACREP
+\else
+\newcommand{\DIRACREP}{}
+
+\usepackage{physics}
+\usepackage{xparse}
+% \input{cosmo/maths}
+
+
+% a macro to typeset representations in bra-ket notation.
+% can be used either with just ket \rep|A> or bra \rep<X|
+% or together, \rep <X||A>
+\NewDocumentCommand{\rep}{s d<| d|>}{%
+% flips starring behavior relative to physics package
+\IfBooleanTF{#1}{
+   \IfValueTF{#2}{
+       \IfValueTF{#3}{\braket{#2}{#3}}{\bra{#2}}
+       }{
+       \IfValueTF{#3}{\ket{#3}}{}
+       }
+   }{
+   \IfValueTF{#2}{
+       \IfValueTF{#3}{\braket*{#2}{#3}}{\bra*{#2}}
+       }{
+       \IfValueTF{#3}{\ket*{#3}}{}
+       }
+   }
+}
+
+% for those who prefer the physics package \bra \ket notation
+\NewDocumentCommand{\rbra}{sm}{\IfBooleanTF{#1}{\rep*<#2|}{\rep<#2|}}
+\NewDocumentCommand{\rket}{sm}{\IfBooleanTF{#1}{\rep*|#2>}{\rep|#2>}}
+\NewDocumentCommand{\rbraket}{smom}{
+    \IfBooleanTF{#1}{
+        \IfNoValueTF{#3}{\rep*<#2||#4>}{\rep*<#2|#3\rep*|#4>}
+    }{
+        \IfNoValueTF{#3}{\rep<#2||#4>}{\rep<#2|#3\rep|#4>}
+    }
+}
+
+% shortcut for CG "our way"
+\NewDocumentCommand{\cg}{m m m}{\rep<#1; #2||#3>}
+
+% macro to typeset a field. very flexible, should allow
+% to describe non-symmetrized fields \field{\rho}
+% fields that are symmetrized just once \field{\rho}x{\nu}
+% equivariant fields \field[lambda mu]{\rho}x2
+% and multi-scale LODE \field{\rho}x{\nu}[V]x{\nu'}
+\NewDocumentCommand{\field}{o m e{_} e{^} o e{_} e{^}}{
+% use overline if an otimes argument is specified, or if there is a double field entry
+\IfValueTF{#5}{\overline{
+  #2\IfValueT{#3}{_#3}\IfValueT{#4}{^{\otimes #4}} % first block
+  \otimes
+  #5\IfValueT{#6}{_#6}\IfValueT{#7}{^{\otimes #7}} % second block
+  \IfValueT{#1}{;#1}
+}}{
+  \IfValueTF{#4}{\overline{
+     #2\IfValueT{#3}{_#3}\IfValueT{#4}{^{\otimes #4}}
+     \IfValueT{#1}{;#1}
+  }}
+  {#2\IfValueT{#3}{_#3}}
+}
+}
+
+% shortcuts for commonly-used fields
+\NewDocumentCommand{\frho}{o e{_} e{^}}{
+\field[#1]{\rho}_{#2}^{#3}
+}
+
+% shortcuts for commonly used feature indices
+
+% generic feature indices
+\newcommand{\Q}[0]{Q}
+\newcommand{\q}[0]{q}
+
+% we use \bx for Cartesian basis, and \br to indicate atom positions
+\newcommand{\br}{\mbf{r}}
+\newcommand{\bx}{\mbf{x}}
+\newcommand{\bxhat}{\hat{\mbf{x}}}
+\newcommand{\brhat}{\hat{\mbf{r}}}
+
+\newcommand{\e}{a}  % element index
+
+\NewDocumentCommand{\ex}{e_}{
+\IfValueTF{#1}{\e_{#1}\bx_{#1}}{\e\bx}
+}  % element index
+
+% common indices for fully discretized density basis, and all sorts of combinations of subindices
+\NewDocumentCommand{\lm}{e_}{
+\IfValueTF{#1}{l_{#1}m_{#1}}{lm}
+}
+\NewDocumentCommand{\nlm}{e_}{
+\IfValueTF{#1}{n_{#1}\lm_{#1}}{n\lm}
+}
+\NewDocumentCommand{\enlm}{e_}{
+\IfValueTF{#1}{\e_{#1}\nlm_{#1}}{\e\nlm}
+}
+\NewDocumentCommand{\en}{e_}{
+\IfValueTF{#1}{\e_{#1}n_{#1}}{\e n}
+}
+% coupled angular momentum basis
+\NewDocumentCommand{\nlk}{e_}{
+\IfValueTF{#1}{n_{#1}l_{#1}k_{#1}}{nlk}
+}
+\NewDocumentCommand{\enlk}{e_}{
+\IfValueTF{#1}{\e_{#1}\nlk_{#1}}{\e\nlk}
+}
+\NewDocumentCommand{\enl}{e_}{
+\IfValueTF{#1}{\en_{#1}l_#1}{\en l}
+}
+
+% SOAP shortcuts - starred version removes ; separators
+\NewDocumentCommand{\nnl}{s}{
+\IfBooleanTF{#1}{n_1 n_2 l}{n_1; n_2; l}
+}
+\NewDocumentCommand{\ennl}{s}{
+\IfBooleanTF{#1}{\en_1 \en_2 l}{\en_1; \en_2; l}
+}
+
+% greek indices for equivariants
+\NewDocumentCommand{\gslm}{s}{
+\IfBooleanTF{#1}{\sigma\lambda\mu}{\sigma;\lambda\mu}
+}
+\NewDocumentCommand{\glm}{}{\lambda\mu}
+
+% other commonly used symbols
+
+% symmetry operations
+\newcommand{\Shat}{\hat{S}}
+\newcommand{\ihat}{\hat{i}}
+\newcommand{\Rhat}{\hat{R}}
+\newcommand{\That}{\hat{t}}
+
+% common convergence parameters
+\newcommand{\nmax}{n_\text{max}}
+\newcommand{\lmax}{l_\text{max}}
+\newcommand{\fcut}[0]{{f_\text{cut}} }
+\newcommand{\rcut}[0]{{r_\text{cut}} }
+\newcommand{\nneigh}[0]{n_\text{neigh}}
+\newcommand{\nfeat}[0]{n_\text{feat}}
+\newcommand{\qmax}[0]{\q_\text{max}}
+\fi %\ifdefined\DIRACREP

cosmo/maths.tex

+%%%%%%%%%%%%%%%%%%% maths.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Standard maths notation that we need to use consistently
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% include guards
+\ifdefined\COSMOMATHS
+\else
+\newcommand{\COSMOMATHS}{}
+% shortcuts for boldface and calligraphic
+\newcommand{\mcal}[1]{\ensuremath{\mathcal{#1}}}
+\newcommand{\mbf}[1]{\ensuremath{\mathbf{#1}}}
+
+%
+
+% integral d
+\newcommand{\D}[1]{\operatorname{d}{\!#1}\,}
+
+% special function that we want to use consistently
+\newcommand{\Ylm}{Y^m_l}
+
+\fi % \ifdefined\COSMOMATHS

cosmo/ml-models.tex

+%%%%%%%%%%%%%%%%%%%  ml-models.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Miscellaneous macros used to typeset quantities that occur in the discussion
+% of machine-learning models
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+% include guards
+\ifdefined\COSMOMODELS
+\else
+\newcommand{\COSMOMODELS}{}
+\usepackage{bm,upgreek}
+
+% generic targets
+\newcommand{\y}[0]{y}
+\newcommand{\yt}[0]{\tilde{y}}
+\newcommand{\by}[0]{\mbf{\y}}
+
+% kernel function, distance function
+\newcommand{\krn}[0]{\operatorname{k}}
+\newcommand{\dst}[0]{\operatorname{d}}
+
+% feature vectors and indices
+\newcommand{\feat}{\upxi}
+\newcommand{\bfeat}[0]{\ensuremath{\bm{\upxi}}}
+\newcommand{\bfeatc}[0]{\ensuremath{\bm{\upchi}}}
+% feature matrix - we use capital xi because X is usually associated with Cartesian coordinates
+\newcommand{\bFeat}{\bm{\Xi}}
+\newcommand{\bvphi}{\bm{\upvarphi}}
+
+% kernels
+\newcommand{\kactive}{M}  % indices referring to the different sets
+\newcommand{\ktrain}{N}
+\newcommand{\bK}{\mbf{K}}
+\newcommand{\KMM}{\bK_{\kactive\kactive}}
+\newcommand{\KNM}{\bK_{\ktrain\kactive}}
+
+% weights
+\newcommand{\w}{w}   % linear regression weights
+\newcommand{\kw}{b}   % kernel weights
+\newcommand{\bw}{\mbf{\w}}
+\newcommand{\bkw}{\mbf{\kw}}
+
+
+
+\fi % \ifdefined\COSMOMODELS

eqn/qm/rydberg.tex

+

fig/aiida-kkr-ml/da/TaCs/plotkkr_TaCs_info.txt

+should all have num atom 15, but plots show convergence not affected
+
+                                      uuid  scale_factor  num_atoms_cluster  \
+1043  21103999-642f-4d99-9fdd-98fd6d1cb959      0.799805                 15   
+1881  2208eeed-fe5e-4ea1-88de-9398695110cc      0.899902                 65   
+2957  3ce1d49c-2c29-46bd-9f1d-732870b1151c      1.000000                 59   
+6110  b2f2a3ab-3cae-48af-8db8-df3343bfb42c      1.099609                 59   
+7763  1086f352-64d8-4880-a411-a9794812453b      1.200195                 15   
+
+      number_of_iterations           rms  
+1043                    23  6.074600e-08  
+1881                    30  7.610200e-08  
+2957                    32  4.988500e-08  
+6110                    33  2.876900e-08  
+7763                    30  4.252900e-08  
+ 
+the comparison plots 0.9, 1.1, 1.2