The presence of deterministic noise in the DFT/MRCI(2) potentials was dealt with approximately via the inclusion of white noise in the GPR kernel. This leads to a fundamental change in interpretation of the optimised points of (near) degeneracy, and the question of the true existence of conical intersections at the DFT/MRCI(2) level of theory. As a result of the noise term, the surrogate surfaces cannot be made arbitrarily accurate with the addition of more data points, thus affecting the level of degeneracy that can be obtained. Despite the issue with explicitly incorporating noise, however, we have shown that the GPR learning of characteristic polynomial coefficients to account for the deterministic noise present in the DFT/MRCI(2) potentials is a viable method that returns sensible surfaces that optimizes easily with direct optimization methods, and yields MECI geometries in excellent agreement with their ab initio MRCI counterparts.