The No-Core Shell Model (NCSM) treats nuclei as systems of non-relativistic point-like nucleons interacting through realistic inter-nucleon interactions. The many-body wave function is cast into an expansion over harmonic-oscillator (HO) basis states containing up to Nmax harmonic oscillator excitations above the lowest Pauli-principle-allowed configuration. Such formulation of the problem allows for calculation of properties of interest such as the nuclear binding energy. In principle the exact result is obtained as Nmax tends to infinity. In practice for the nuclei under consideration the calculation is expected to converge for Nmax of around 20, however world’s largest supercomputers allow for performing calculations with Nmax<16 in practical timescales, therefore an effective extrapolation method is needed. Since the properties of the binding energy calculation are known, but not the exact functional form of the binding energy as a function of Nmax, we attempt to extrapolate the binding energy calculation using Gaussian Processes (GP). The generic GP Regression is unlikely to be informative as we lack data over a large region in Nmax,however by imposing constraints on first and second derivative of the function we hope to obtain an estimate of binding energy with well understood uncertainty at high Nmax. The GP posterior can be written to incorporate the constraints at several design points. Previous work in the literature demonstrated successful application of first derivative constraints, we attempt to extend this work to second derivatives and implement the Sequential Monte Carlo method necessary for performing the calculation.