We present a method for reconstructing coherent deflections of ultra-high-energy cosmic ray arrival directions that are expected from propagation through cosmic magnetic fields. Concretely, we apply a data-driven approach that searches for deflection patterns simultaneously in every sky direction from the individual cosmic ray arrival directions and energies that can be measured, for example, at the Pierre Auger Observatory.
For that, we parameterize the deflections using a spherical harmonic expansion in combination with a variable magnetic field strength. The coefficients for the field orientations and strengths are adapted using a likelihood-free Bayesian approach based on normalizing flows. This allows for a straightforward assessment of the uncertainty on the predicted deflection in every sky direction. We evaluate the method's sensitivity to identify and parameterize the presence of coherent magnetic field deflections on realistic simulated astrophysical scenarios.