Multi-output Gaussian processes for the reconstruction of homogenized cross-sections

Special Issue on ‘Overview of recent advances in HPC simulation methods for nuclear applications’, edited by Andrea Zoia, Elie Saikali, Cheikh Diop and Cyrille de Saint Jean

Open Access

Table 2.

Description of the Lazy-LMC model. For each parameter featured in the definition of the LMC (Eq. (5)), a procedure is given to set its value to an adequate one. See Section 2.3 for more information.

Term	Description	Procedure to set value or neutralize
m_j(⋅)	Mean function of the j-th regression task	Set to 0

$ϵ_{j} \sim N (0, σ_{j}^{2} I_{n})$ $\epsilon_{j} \sim \mathcal{N}(0,\sigma_{j}^{2}\, {\mathbf{I}_{\mathbf{n}}})$	Noise of the j-th task	Set to a small value (10⁻⁴). A noise of this magnitude is also added to the latent processes during interpolation

H	Matrix mixing latent processes into observable signals	Set to the q first left singular vectors, multiplied by their associated singular values, of the data matrix Y

k_i	Kernel of the i-th latent process u_i	Chosen to be the parameter-free cubic spline kernel of Equation (6)

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