API Reference

ActiveSubspace{T<:Real} <: DimensionReducer
    Q :: Function 
    ∇Q :: Function (gradient of Q)
    tol :: T

Use the theory of active subspaces, with a given quantity of interest (expressed as the function Q) which takes a Configuration as an input and outputs a real scalar. ∇Q should input a Configuration and output an appropriate gradient. If tol is a float then the number of components to keep is determined by the smallest n such that relative percentage of variance explained by keeping the leading n principle components is greater than 1 - tol. If tol is an int, then we return the components corresponding to the tol largest eigenvalues.

AtomicData <: Data

Abstract type declaring the type of information that is unique to a particular atom (instead of a whole configuration).

Configuration(data::Union{AtomsBase.FlexibleSystem, ConfigurationData} )

A Configuration is a data struct that contains information unique to a particular configuration of atoms (Energy, LocalDescriptors, ForceDescriptors, and a FlexibleSystem) in a dictionary. Example: '''julia e = Energy(-0.57, u"eV") ld = LocalDescriptors(...) c = Configuration(e, ld) '''

Configurations can be added together, which merges the data dictionaries '''julia c1 = Configuration(e) # Contains energy c2 = Configuration(f) # contains forces c = c1 + c2 # c <: Configuration, contains energy and forces '''

ConfigurationData <: Data

Abstract type declaring the type of data that is unique to a particular configuration (instead of just an atom).

CorrelationMatrix 
    α :: Vector{Float64} # weights

CorrelationMatrix produces a global descriptor that is the correlation matrix of the local descriptors. In other words, it is mean(bi'*bi for bi in B).

struct CovariateLinearProblem{T<:Real} <: LinearProblem{T} e::Vector f::Vector{Vector{T}} B::Vector{Vector{T}} dB::Vector{Matrix{T}} β::Vector{T} β0::Vector{T} σe::Vector{T} σf::Vector{T} Σ::Symmetric{T,Matrix{T}} end

A CovariateLinearProblem is a linear problem in which we are fitting energies and forces using both descriptors and their gradients (B and dB, respectively). When this is the case, the solution is not available analytically and must be solved using some iterative optimization proceedure. In the end, we fit the model coefficients, β, standard deviations corresponding to energies and forces, σe and σf, and the covariance Σ.

struct DBSCANSelector <: SubsetSelector
    clusters
    eps
    minpts
    sample_size
end

Definition of the type DBSCANSelector, a subselector based on the clustering method DBSCAN.

function DBSCANSelector(
    ds::DataSet,
    eps,
    minpts,
    sample_size
)

Constructor of DBSCANSelector based on the atomic configurations in ds, the DBSCAN params eps and minpts, and the sample size sample_size.

Data

Abstract supertype of ConfigurationData.

DataBase

Abstract type for DataSets.

DataSet

Struct that holds vector of configuration. Most operations in PotentialLearning are built around the DataSet structure.

Distance

A struct of abstract type Distance produces the distance between two `global` descriptors, or features. Not all distances might be compatible with all types of features.

Divergence

A struct of abstract type Divergence produces a measure of discrepancy between two probability distributions. Discepancies may take as argument analytical distributions or sets of samples representing empirical distributions.

DotProduct <: Kernel 
    α :: Power of DotProduct kernel 


Computes the dot product kernel between two features, i.e.,

cos(θ) = ( A ⋅ B / (||A||^2||B||^2) )^α

Energy <: ConfigurationData
    d :: Real
    u :: Unitful.FreeUnits

Convenience struct that holds energy information (and corresponding units). Default unit is eV

Euclidean <: Distance 
    Cinv :: Covariance Matrix 

Computes the squared euclidean distance with weight matrix Cinv, the inverse of some covariance matrix.

ExtXYZ <: IO

Feature

A struct of abstract type Feature represents a function that takes in a set of local descriptors corresponding to some atomic environment and produce a global descriptor.

Force <: AtomicData 
    f :: Vector{<:Real}
    u :: Unitful.FreeUnits

Contains the force with (x,y,z)-components in f with units u. Default unit is "eV/Å".

ForceDescriptor <: AtomicData
    b :: Vector{<:Vector{<:Real}}

Contains the x,y,z components (out vector) of the force descriptor (inner vector).

ForceDescriptors <: ConfigurationData
    b :: Vector{ForceDescriptor}

A container holding all of the ForceDescriptors for all atoms in a configuration.

Forces <: ConfigurationData
    f :: Vector{force}

Forces is a struct that contains all force information in a configuration.

Forstner <: Distance 
    α :: Regularization parameter

Computes the squared Forstner distance between two positive semi-definite matrices.

    GlobalMean{T}

GlobalMean produces the mean of the local descriptors.

    GlobalSum{T}

GlobalSum produces the sum of the local descriptors.

InverseMultiquadric <: Kernel 
    d :: Distance function 
    c2 :: Squared constant parameter
    ℓ :: Length-scale parameter

Computes the inverse multiquadric (IMQ) kernel, i.e.,

 k(A, B) = (c^2 + d(A,B)/β^2)^{-1/2}

Kernel

A struct of abstract type Kernel is function that takes in two features and produces a semi-definite scalar representing the similarity between the two features.

KernelSteinDiscrepancy <: Divergence
    score :: Function
    knl :: Kernel

Computes the kernel Stein discrepancy between distributions p (from which samples are provided) and q (for which the score is provided) based on the RKHS defined by kernel k.

struct LAMMPS <: IO
    elements :: Vector{Symbol}
    boundary_conditions :: Vector
end

struct LearningProblem{T<:Real} <: AbstractLearningProblem ds::DataSet logprob::Function ∇logprob::Function params::Vector{T} end

Generic LearningProblem that allows the user to pass a logprob(y::params, ds::DataSet) function and its gradient. The gradient should return a vector of logprob with respect to it's params. If the user does not have a gradient function available, then Flux can provide one for it (provided that logprob is of the form above).

function LearningProblem( ds::DataSet, logprob::Function, params::Vector{T} ) where {T}

Generic LearningProblem construnctor.

abstract type LinearProblem{T<:Real} <: AbstractLearningProblem end

An abstract type to specify linear potential inference problems.

function LinearProblem( ds::DataSet; T = Float64 )

Construct a LinearProblem by detecting if there are energy descriptors and/or force descriptors and construct the appropriate LinearProblem (either Univariate, if only a single type of descriptor, or Covariate, if there are both types).

LocalDescriptor <: AtomicData

A vector corresponding to the descriptor for a particular atom's neighborhood.

LocalDescriptors <: ConfigurationData

A vector of LocalDescriptor, which now should represent all local descriptors for atoms in a configuration.

PCA <: DimensionReducer
    tol :: Float64

Use SVD to compute the PCA of the design matrix of descriptors. (using Force descriptors TBA)

If tol is a float then the number of components to keep is determined by the smallest n such that relative percentage of variance explained by keeping the leading n principle components is greater than 1 - tol. If tol is an int, then we return the components corresponding to the tol largest eigenvalues.

RBF <: Kernel 
    d :: Distance function 
    α :: Regularization parameter 
    ℓ :: Length-scale parameter
    β :: Scale parameter


Computes the squared exponential kernel, i.e.,

 k(A, B) = β xp( -rac{1}{2} d(A,B)/ℓ^2 ) + α δ(A, B)

struct Random
    num_configs :: Int 
    batch_size  :: Int 
end

A convenience function that allows the user to randomly select indices uniformly over [1, num_configs].

struct UnivariateLinearProblem{T<:Real} <: LinearProblem{T} ivdata::Vector dvdata::Vector β::Vector{T} β0::Vector{T} σ::Vector{T} Σ::Symmetric{T,Matrix{T}} end

A UnivariateLinearProblem is a linear problem in which there is only 1 type of independent variable / dependent variable. Typically, that means we are either only fitting energies or only fitting forces. When this is the case, the solution is available analytically and the standard deviation, σ, and covariance, Σ, of the coefficients, β, are computable.

YAML <: IO
    energy_units :: Unitful.FreeUnits
    distance_units :: Unitful.FreeUnits

struct kDPP
    K :: EllEnsemble
end

A convenience function that allows the user access to a k-Determinantal Point Process through Determinantal.jl. All that is required to construct a kDPP is a similarity kernel, for which the user must provide a LinearProblem and two functions to compute descriptor (1) diversity and (2) quality.

kDPP(ds::Dataset, f::Feature, k::Kernel)

A convenience function that allows the user access to a k-Determinantal Point Process through Determinantal.jl. All that is required to construct a kDPP is a dataset, a method to compute features, and a kernel. Optional arguments include batch size and type of descriptor (default LocalDescriptors).

kDPP(features::Union{Vector{Vector{T}}, Vector{Symmetric{T, Matrix{T}}}}, k::Kernel)

A convenience function that allows the user access to a k-Determinantal Point Process through Determinantaljl. All that is required to construct a kDPP are features (either a vector of vector features or a vector of symmetric matrix features) and a kernel. Optional argument is batch_size (default length(features)).

function computeforcedescriptors( ds::DataSet, basis::BasisSystem; pbar = true )

Compute force descriptors of a basis system and dataset using threads.

function computelocaldescriptors( ds::DataSet, basis::BasisSystem; pbar = true )

ds: dataset. basis: basis system (e.g. ACE) pbar: progress bar

Compute local descriptors of a basis system and dataset using threads.

KernelMatrix(ds1::DataSet, ds2::DataSet, F::Feature, k::Kernel)

Compute nonsymmetric kernel matrix K using features of the datasets ds1 and ds2 calculated using the Feature method F.

KernelMatrix(ds::DataSet, F::Feature, k::Kernel)

Compute symmetric kernel matrix K using features of the dataset ds calculated using the Feature method F.

KernelMatrix(F, k::Kernel)

Compute symmetric kernel matrix K where K{ij} = k(Fi, F_j).

KernelMatrix(F1, F2, k::Kernel)

Compute non-symmetric kernel matrix K where K{ij} = k(F1i, F2_j).

function calc_centroid(
    m::Array{Float64,2}
)

Calculate a centroid of a matrix.

calc_metrics(x_pred, x)

x_pred: vector of predicted values of a variable. E.g. energy. x: vector of true values of a variable. E.g. energy.

Returns MAE, RMSE, and RSQ.

compute_distance(A, B, d)

Compute the distance between features A and B using distance metric d.

compute_feature(ds::DataSet, f::Feature; dt = LocalDescriptors)

Computes features of the dataset ds using the feature method F on descriptors dt (default option are the LocalDescriptors, if available).

compute_gradx_distance(A, B, d)

Compute gradient of the distance between features A and B using distance metric d, with respect to the first argument (A).

compute_gradx_kernel(A, B, k)

Compute gradient of the kernel between features A and B using kernel k, with respect to the first argument (A).

compute_gradxy_distance(A, B, d)

Compute second-order cross derivative of the distance between features A and B using distance metric d.

compute_gradxy_kernel(A, B, k)

Compute the second-order cross derivative of the kernel between features A and B using kernel k.

compute_grady_distance(A, B, d)

Compute gradient of the distance between features A and B using distance metric d, with respect to the second argument (B).

compute_grady_kernel(A, B, k)

Compute gradient of the kernel between features A and B using kernel k, with respect to the second argument (B).

compute_kernel(A, B, k)

Compute similarity kernel between features A and B using kernel k.

function distance_matrix_kabsch(
    ds::DataSet
)

Calculate a matrix of distances between atomic configurations using KABSCH method.

function distance_matrix_periodic(
    ds::DataSet
)

Calculates a matrix of distances between atomic configurations taking into account the periodic boundaries.

fit(ds::DataSet, dr::DimensionReducer)

Fits a linear dimension reduction routine using information from DataSet. See individual types of DimensionReducers for specific details.

fit(ds::DataSet, as::ActiveSubspace)

Fits a linear dimension reduction routine using the eigendirections of the uncentered covariance of the function ∇Q(c::Configuration) over the configurations in ds. Primarily used to reduce the dimension of the descriptors.

fit(ds::DataSet, pca::PCA)

Fits a linear dimension reduction routine using PCA on the global descriptors in the dataset ds.

fit_transform(ds::DataSet, dr::DimensionReducer)

Fits a linear dimension reduction routine using information from DataSet and performs dimension reduction on descriptors and force_descriptors (whichever are available). See individual types of DimensionReducers for specific details.

function force( c::Configuration, bp::BasisPotential )

c: atomic configuration. bp: basis potential.

function force( c::Configuration, nnbp::NNBasisPotential )

c: atomic configuration. nnbp: neural network basis potential.

function get_all_energies(
    ds::DataSet,
    bp::BasisPotential
)

ds: dataset. bp: basis potential.

function getallenergies( ds::DataSet )

ds: dataset.

function getallforces( ds::DataSet, bp::BasisPotential )

ds: dataset. bp: basis potential.

function get_all_forces(
    ds::DataSet
)

ds: dataset.

get_batches(n_batches, B_train, B_train_ext, e_train, dB_train, f_train,
            B_test, B_test_ext, e_test, dB_test, f_test)

n_batches: no. of batches per dataset. B_train: descriptors of the energies used in training. B_train_ext: extendended descriptors of the energies used in training. Requiered to compute forces. e_train: energies used in training. dB_train: derivatives of the energy descritors used in training. f_train: forces used in training. B_test: descriptors of the energies used in test. B_test_ext: extendended descriptors of the energies used in test. Requiered to compute forces. e_test: energies used in test. dB_test: derivatives of the energy descritors used in test. f_test: forces used in test.

Returns the data loaders for training and test of energies and forces.

function get_clusters(
    ds,
    eps,
    minpts
)

Computes clusters from the configurations in ds using DBSCAN with parameters eps and minpts.

get_dpp_mode(dpp::kDPP, batch_size::Int) <: Vector{Int64}

Access an approximate mode of the k-DPP as calculated by a greedy subset algorithm. See Determinantal.jl for details.

get_energy(c::Configuration) <: Energy

Retrieves the energy (if available) in the Configuration c.

get_force_descriptors(c::Configuration) <: ForceDescriptors

Retrieves the force descriptors (if available) in the Configuration c.

get_forces(c::Configuration) <: Forces

Retrieves the forces (if available) in the Configuration c.

get_inclusion_prob(dpp::kDPP) <: Vector{Float64}

Access an approximation to the inclusion probabilities as calculated by Determinantal.jl (see package for details).

get_input(args)

args: vector of arguments (strings)

Returns an OrderedDict with the arguments. See https://github.com/cesmix-mit/AtomisticComposableWorkflows documentation for information about how to define the input arguments.

get_local_descriptors(c::Configuration) <: LocalDescriptors

Retrieves the local descriptors (if available) in the Configuration c.

get_metrics( e_train_pred, e_train, f_train_pred, f_train,
             e_test_pred, e_test, f_test_pred, f_test,
             B_time, dB_time, time_fitting)

e_train_pred: vector of predicted training energy values. e_train: vector of true training energy values. f_train_pred: vector of predicted training force values. f_train: vector of true training force values. e_test_pred: vector of predicted test energy values. e_test: vector of true test energy values. f_test_pred: vector of predicted test force values. f_test: vector of true test force values. B_time: elapsed time consumed by descriptors calculation. dB_time: elapsed time consumed by descriptor derivatives calculation. time_fitting: elapsed time consumed by fitting process.

Computes MAE, RMSE, and RSQ for training and testing energies and forces. Also add elapsed times about descriptors and fitting calculations. Returns an OrderedDict with the information above.

get_metrics( e_train_pred, e_train, e_test_pred, e_test)

e_train_pred: vector of predicted training energy values. e_train: vector of true training energy values. e_test_pred: vector of predicted test energy values. e_test: vector of true test energy values.

Computes MAE, RMSE, and RSQ for training and testing energies. Returns an OrderedDict with the information above.

get_metrics(
    x_pred,
    x;
    metrics = [mae, rmse, rsq],
    label = "x"
)

x_pred: vector of predicted forces, x: vector of true forces. metrics: vector of metrics. label: label used as prefix in dictionary keys.

Returns and OrderedDict with different metrics.

get_positions(c::Configuration) <: Vector{SVector}

Retrieves the AtomsBase system positions (if available) in the Configuration c.

get_random_subset(r::Random, batch_size :: Int) <: Vector{Int64}

Access a random subset of the data as sampled from the provided k-DPP. Returns the indices of the random subset and the subset itself.

function get_random_subset(
    s::DBSCANSelector,
    batch_size = s.sample_size
)

Returns a random subset of indexes composed of samples of size batch_size ÷ length(s.clusters) from each cluster in s.

get_random_subset(dpp::kDPP, batch_size :: Int) <: Vector{Int64}

Access a random subset of the data as sampled from the provided k-DPP. Returns the indices of the random subset and the subset itself.

get_system(c::Configuration) <: AtomsBase.AbstractSystem

Retrieves the AtomsBase system (if available) in the Configuration c.

get_values(e::Energy) <: Real

Get the underlying real value (= e.d)

get_values(v::SVector)

Removes units from a position.

function kabsch(
    reference::Array{Float64,2},
    coords::Array{Float64,2}
)

Input: two sets of points: reference, coords as Nx3 Matrices (so) Returns optimally rotated matrix

function kabsch_rmsd(
    P::Array{Float64,2},
    Q::Array{Float64,2}
)

Directly return RMSD for matrices P, Q for convenience.

function learn!( iap::InteratomicPotentials.LinearBasisPotential, ds::DataSet, args... )

Learning dispatch function, common to ordinary and weghted least squares implementations.

function learn!( lp::CovariateLinearProblem, α::Real )

Fit a Gaussian distribution by finding the MLE of the following log probability: ℓ(β, σe, σf) = -0.5(e - A_e *β)'(e - Ae * β) / σe - 0.5*(f - Af β)'(f - A_f * β) / σf - log(σe) - log(σf)

through an optimization procedure.

function learn!( lp::CovariateLinearProblem, ss::SubsetSelector, α::Real; num_steps=100, opt=Flux.Optimise.Adam() )

Fit a Gaussian distribution by finding the MLE of the following log probability: ℓ(β, σe, σf) = -0.5(e - A_e *β)'(e - Ae * β) / σe - 0.5*(f - Af β)'(f - A_f * β) / σf - log(σe) - log(σf)

through an iterative batch gradient descent optimization proceedure where the batches are provided by the subset selector.

function learn!( lp::CovariateLinearProblem, ws::Vector, int::Bool )

Fit energies and forces using weighted least squares.

function learn!( lp::LearningProblem, ss::SubsetSelector; num_steps = 100::Int, opt = Flux.Optimisers.Adam() )

Attempts to fit the parameters lp.params in the learning problem lp using batch gradient descent with the optimizer opt and num_steps number of iterations. Batching is provided by the passed ss::SubsetSelector.

function learn!( lp::LearningProblem; num_steps=100::Int, opt=Flux.Optimisers.Adam() )

Attempts to fit the parameters lp.params in the learning problem lp using gradient descent with the optimizer opt and num_steps number of iterations.

function learn!( lp::LinearProblem )

Default learning problem: weighted least squares.

function learn!( lp::UnivariateLinearProblem, α::Real )

Fit a univariate Gaussian distribution for the equation y = Aβ + ϵ, where β are model coefficients and ϵ ∼ N(0, σ). Fitting is done via SVD on the design matrix, A'*A (formed iteratively), where eigenvalues less than α are cut-off.

function learn!( lp::UnivariateLinearProblem, ss::SubsetSelector, α::Real; num_steps = 100, opt = Flux.Optimise.Adam() )

Fit a univariate Gaussian distribution for the equation y = Aβ + ϵ, where β are model coefficients and ϵ ∼ N(0, σ). Fitting is done via batched gradient descent with batches provided by the subset selector and the gradients are calculated using Flux.

function learn!( lp::UnivariateLinearProblem, ws::Vector, int::Bool )

Fit energies using weighted least squares.

linearize_forces(forces)

forces: vector of forces per system

Returns a vector with the components of the forces of the systems.

load_data(file::string, extxyz::ExtXYZ)
Load configuration from an extxyz file into a DataSet

load_data(file::string, yaml::YAML)

Load configurations from a yaml file into a Vector of Flexible Systems, with Energies and Force.
Returns 
    ds - DataSet
    t = Vector{Dict} (any miscellaneous info from yaml file)

load_datasets(input)

input: OrderedDict with input arguments. See get_defaults_args().

Returns training and test systems, energies, forces, and stresses.

mae(x_pred, x)

x_pred: vector of predicted values. E.g. predicted energies. x: vector of true values. E.g. DFT energies.

Returns mean absolute error.

mean_cos(x_pred, x)

x_pred: vector of predicted forces, x: vector of true forces.

Returns mean cosine.

function periodic_rmsd(
    p1::Array{Float64,2},
    p2::Array{Float64,2},
    box_lengths::Array{Float64,1}
)

Calculates the RMSD between atom positions of two configurations taking into account the periodic boundaries.

function potential_energy( c::Configuration, bp::BasisPotential )

c: atomic configuration. bp: basis potential.

function potential_energy( c::Configuration, nnbp::NNBasisPotential )

c: atomic configuration. nnbp: neural network basis potential.

function rmsd(
    A::Array{Float64,2},
    B::Array{Float64,2}
)

Calculate root mean square deviation of two matrices A, B. See http://en.wikipedia.org/wiki/Root-mean-squaredeviationofatomicpositions

rmse(x_pred, x)

x_pred: vector of predicted values. E.g. predicted energies. x: vector of true values. E.g. DFT energies.

Returns mean root mean square error.

rsq(x_pred, x)

x_pred: vector of predicted values. E.g. predicted energies. x: vector of true values. E.g. DFT energies.

Returns R-squared.

function sample(
    c,
    batch_size
)

Select from cluster c a sample of size batch_size.

to_num(str)

str: string with a number: integer or float

Returns an integer or float.

function translate_points(
    P::Array{Float64,2},
    Q::Array{Float64,2}
)

Translate P, Q so centroids are equal to the origin of the coordinate system Translation der Massenzentren, so dass beide Zentren im Ursprung des Koordinatensystems liegen