Atmospheric sounding from a space instrument usually leads to solving some inverse problem to retrieve a vertical number density profile of a particular constituent like ozone. The paper starts to consider the total number of calls to the forward model that are necessary to iteratively process a large ensemble of observations. For a comparable computational effort, it can be useful to generate a large ensemble of synthetic cases and the associated principal components for both state vector and measurement vector spaces. Then, a direct inverse mapping is obtained by a nonlinear regression through an artificial neural network. The inversion operator is accurate and robust to noise. A test bench is to apply this direct method to the OMPS-LP limb data and to compare the performances with two other published retrieval algorithms. The inter-comparison turns out to be statistically meaningful for a full month of data. Measurement errors are estimated by a Monte-Carlo approach, and averaging kernels are computed with two different methods.