Training and Mapping Workflow

CiderPress supplies feature, covariance, fitting, and mapping primitives for constructing CIDER models with Gaussian process regression. Reference calculations, dataset assembly, and job scheduling are external to the model layer.

Electronic data expected by the model layer

For each electronic system, the training layer consumes arrays generated with one consistent feature definition:

  • quadrature weights and spin-resolved semilocal density ingredients;

  • normalized descriptor blocks in their serialized order;

  • total-energy and XC baseline terms used to form the training target;

  • exact-exchange values when exchange is an explicit training target;

  • orbital-occupation derivatives when eigenvalue data are included; and

  • optional correction values and metadata associated with the reference calculation.

ElectronAnalyzer and the descriptor tools in Inspecting Densities and Descriptors provide these electronic arrays. Their stored geometry, basis or PAW representation, density-generating functional, grid, spin, and orbital conventions define the metadata of a system record.

Integrated observations

CIDER fits integrated energies and their linear combinations (as opposed to the energy densities directly predicted by the model). This allows one to fit the total XC energies of chemical systems and relative energies of chemical systems, which can be applied to fitting reaction energies, barrier heights, interaction energies, equations of state, ionization potentials, and more. In CiderPress, all these properties are expressed as linear combinations of the energies of chemical systems and referred to as “reactions.” A reaction record gives the member identifiers, stoichiometric coefficients, reference energy, unit conversion, and observation noise. The model evaluates the explicit Kohn–Sham and additive baseline contributions on the same systems, then fits the residual assigned to the learned component.

It is also possible to fit the derivative of a system’s energy with respect the occupation number of a given Kohn-Sham orbital (along with linear combinations of these derivatives) within the same reaction framework described above. This approach enables direct fitting of orbital properties like band gaps. [1]

A DFTKernel couples transformed descriptors to a differentiable covariance kernel, an energy multiplier, an additive baseline, and a control-point set. DFTKernel2 supplies the libxc-based baseline interface used by full-XC models. Multiple kernels can represent separate exchange and correlation terms and contribute to the same reaction labels.

Sparse Gaussian-process fit

For each kernel, integrated covariances with the control points form the columns of Kmn. Kmm is the covariance matrix among control points. The system covariance is

\[\mathbf K_\mathrm{sys} = \mathbf K_{mn}^{\mathsf T}\mathbf K_{mm}^{-1}\mathbf K_{mn}.\]

Independent learned components contribute additive system covariance matrices. ciderpress.models.train.MOLGP.fit() solves their shared noisy system problem and converts the resulting system weights into one set of control-point coefficients per kernel. The complete predictive-mean derivation is in Machine Learning Framework for CIDER Functionals.

A typical construction sequence is:

  1. Create feature settings, normalizers, transforms, and differentiable kernels.

  2. Select control points that cover the transformed feature distribution.

  3. Store each system’s integrated covariance, explicit baseline, and any requested occupation derivatives.

  4. Assemble reaction or constraint observations with their units and noise.

  5. Fit the shared system covariance problem.

  6. Map each kernel to its selected inference evaluator and validate the mapped object.

Self-consistent full-XC training

For a full-XC reaction-energy model, orbital relaxation changes the density and therefore the descriptors, baselines, and residual labels. An iterative workflow can regenerate those quantities on densities produced by the current model and refit the GP. Comparisons between fixed-density and self-consistent predictions measure convergence of that outer procedure.

The CIDER26XC work uses this approach together with reaction-specific noise and uniform-electron-gas constraints. [2] Dataset selection, weighting policy, hyperparameter selection, and stopping criteria are inputs supplied by the surrounding training workflow.

Mapping and validation

The mapping step creates the inference evaluator described in Model Objects and Mapping. Mapping tests compare pointwise energies and derivatives, integrated fixed-density values, self-consistent composition, serialized metadata, and backend derivatives at matching numerical settings. The published artifact adds a stable filename and checksum.

The relevant APIs are ciderpress.models.train, ciderpress.models.dft_kernel, ciderpress.models.kernels, and ciderpress.models.kernel_plans.kernel_tools.