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Recent pulsar timing array (PTA) analyses show evidence for a gravitational wave background (GWB) with angular correlations consistent with the Hellings-Downs curve. Anisotropies are a key discriminator of the origin of this GWB, as they are expected to be at 1%─20% for astrophysical sources, but suppressed for cosmological GWBs. However, contrary to gravitational wave detectors at higher frequencies, PTAs only take a few independent measurements of a GWB and consequently are highly sensitive to cosmic variance, which induces apparent anisotropies in individual realizations of an isotropic GWB. We demonstrate explicitly that statistical inference nevertheless remains robust, i.e., measurements are consistent with the underlying assumption of isotropy. This confirms that searches for anisotropies will be able to robustly discriminate astrophysical from cosmological GWBs. To this end, we demonstrate that the maximum multipole constrained by a PTA dataset scales linearly with the number of pulsars <inline-formula><mml:math><mml:mrow><mml:msub><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mi>max</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>.

We present cosmo_learn, an open-source python-based software package designed to simulate cosmological data and perform data-driven inference using a range of modern statistical and machine learning techniques. Motivated by the growing complexity of cosmological models and the emergence of observational tensions, cosmo_learn provides a standardized and flexible framework for benchmarking cosmological inference methods. The package supports realistic noise modeling for key observables in the late Universe, including cosmic chronometers, supernovae Ia, baryon acoustic oscillations, redshift space distortions, and gravitational wave bright sirens. We demonstrate the internal consistency of the simulated data with the input cosmology via residuals and parameter recovery using a fiducial wCDM model. Built-in learning and inference modules include traditional Markov Chain Monte Carlo, as well as more recent approaches such as genetic algorithms, Gaussian processes, Bayesian ridge regression, and artificial neural networks. These methods are implemented in a modular and extensible architecture designed to facilitate comparisons across inference strategies in a common pipeline. By providing a flexible and transparent simulation and learning environment, cosmo_learn supports both educational and research efforts at the intersection of cosmology, statistics, and machine learning.