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Gaussian Process Regression

Group /input/model/unit_XXX/particle_type_ZZZ/adsorption – ADSORPTION_MODEL = GAUSSIAN_PROCESS_REGRESSION

For information on model equations, refer to Gaussian Process Regression.

IS_KINETIC

Selects kinetic or quasi-stationary adsorption mode: 1 = kinetic, 0 = quasi-stationary. If a single value is given, the mode is set for all bound states. Otherwise, the adsorption mode is set for each bound state separately.

Type: int

Range: {0,1}

Length: 1/NTOTALBND

CP_NDIM

Number of input dimensions per training point used in CP_VALS. Must equal number of components, user sanity check.

Type: int

Range: NCOMP

Length: 1

CS_NDIM

Number of output dimensions per training point used in CS_VALS. Must equal total number of bound states, user sanity check.

Type: int

Range: NTOTALBOUND

Length: 1

CP_VALS

Flattened pore-phase concentration training inputs used by the Gaussian process regression model. The values represent the training input points \(X\) used to evaluate the kernel function. The array is interpreted as an NTRAIN major vector.

Unit: \(mol~m_{MP}^{-3}\)

Type: double

Range: unrestricted

Length: NTRAIN * CP_NDIM

CS_VALS

Solid-phase training targets corresponding to CP_VALS. These values form the training output vector used to compute the GPR coefficient vector \(\alpha = (K + \sigma_n^2 I)^{-1} y\).

Unit: \(mol~m_{SP}^{-3}\)

Type: double

Range: unrestricted

Length: NTRAIN * CS_NDIM

GPR_KKIN

Linear-driving-force coefficients in component-major ordering.

Unit: \(s^{-1}\)

Type: double

Range: \(\geq 0\)

Length: NCOMP

KERNEL

Selects the kernel function used by the Gaussian process regression model. Supported values are MLP, RBF, RBF_Linear, and MLP_Linear.

Type: string

Range: {MLP, RBF, RBF_Linear, MLP_Linear}

Length: 1

Kernel-Specific Hyperparameters

Each bound state requires its own kernel configuration specified using the suffix _BNDXXX, where XXX is the zero-padded bound state index (e.g., _BND000, _BND001, _BND002).

Bound state indices are assigned sequentially across components: if component 0 has 2 bound states and component 1 has 1 bound state, the indices are:

• Bound state 0: component 0, state 0

• Bound state 1: component 0, state 1

• Bound state 2: component 1, state 0

The following table summarizes which parameters are required for each kernel:

Kernel	MLP	RBF	RBF_Linear	MLP_Linear
MLP_WEIGHT_VARIANCE_BND_XXX	✓	—	—	✓
MLP_BIAS_VARIANCE_BND_XXX	✓	—	—	✓
MLP_VARIANCE_BND_XXX	✓	—	—	✓
RBF_VARIANCE_BND_XXX	—	✓	✓	—
RBF_LENGTHSCALE_BND_XXX	—	✓	✓	—
LINEAR_VARIANCE_BND_XXX	—	—	✓	✓
GAUSSIAN_NOISE_VARIANCE_BND_XXX	✓	✓	✓	✓

MLP_WEIGHT_VARIANCE_BND_XXX

Weight variance hyperparameter for the MLP (arc-cosine) kernel. Required for MLP and MLP_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

MLP_BIAS_VARIANCE_BND_XXX

Bias variance hyperparameter for the MLP (arc-cosine) kernel. Required for MLP and MLP_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

MLP_VARIANCE_BND_XXX

Output variance hyperparameter for the MLP (arc-cosine) kernel. Required for MLP and MLP_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

RBF_VARIANCE_BND_XXX

Output variance hyperparameter for the RBF (squared exponential) kernel. Required for RBF and RBF_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

RBF_LENGTHSCALE_BND_XXX

Lengthscale hyperparameter for the RBF kernel, expected as \(\ell^2\) (squared lengthscale as exported from scikit-learn). Required for RBF and RBF_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

LINEAR_VARIANCE_BND_XXX

Variance hyperparameter for the linear kernel. Required for RBF_Linear and MLP_Linear kernels.

Type: double

Range: \(\geq 0\)

Length: 1

GAUSSIAN_NOISE_VARIANCE_BND_XXX

Noise variance hyperparameter \(\sigma_n^2\) added to the kernel diagonal for numerical stability and observation noise modeling. Required for all kernel types.

Type: double

Range: \(> 0\)

Length: 1