Context. In the near future, dedicated telescopes will observe Earth-like exoplanets in reflected parent starlight, allowing their physical characterization. Because of the huge distances, every exoplanet will remain an unresolved, single pixel, but temporal variations in the pixel’s spectral flux contain information about the planet’s surface and atmosphere.

Aims. We tested convolutional neural networks for retrieving a planet’s rotation axis, surface, and cloud map from simulated single-pixel observations of flux and polarization light curves. We investigated the influence of assuming that the reflection by the planets is Lambertian in the retrieval while in reality their reflection is bidirectional, and the influence of including polarization.

Methods. We simulated observations along a planet’s orbit using a radiative transfer algorithm that includes polarization and bidirectional reflection by vegetation, deserts, oceans, water clouds, and Rayleigh scattering in six spectral bands from 400 to 800 nm, at various levels of photon noise. The surface types and cloud patterns of the facets covering a model planet are based on probability distributions. Our networks were trained with simulated observations of millions of planets before retrieving maps of test planets.

Results. The neural networks can constrain rotation axes with a mean squared error (MSE) as small as 0.0097, depending on the orbital inclination. On a bidirectionally reflecting planet, 92% of ocean facets and 85% of vegetation, deserts, and cloud facets are correctly retrieved, in the absence of noise. With realistic amounts of noise, it should still be possible to retrieve the main map features with a dedicated telescope. Except for face-on orbits, a network trained with Lambertian reflecting planets yields significant retrieval errors when given observations of bidirectionally reflecting planets, in particular, brightness artifacts around a planet’s pole. Including polarization improves the retrieval of the rotation axis and the accuracy of the retrieval of ocean and cloudy map facets.