  Paleoclimatic measurements serve to understand geophysical processes and
evaluate climate model performances. However, their spatial coverage is
generally sparse and unevenly distributed across the globe. Statistical
interpolation methods are the prevalent techniques to grid such data, but these
purely data-driven approaches sometimes produce results that are incoherent
with our knowledge of the physical world. Physics-Informed Neural Networks
(PINNs) follow an innovative approach to data analysis and physical modeling
through machine learning, as they incorporate physical principles into the
data-driven learning process. Here, we develop PINNs to reconstruct global maps
of atmospheric dust surface deposition fluxes from measurement data in
paleoclimatic archives, for the Holocene and Last Glacial Maximum periods. We
design an advection-diffusion equation to consider dominant wind directions at
various latitudes, which prevents dust particles from flowing upwind. Our PINN
improves on standard kriging interpolation by allowing variable asymmetry
around data points. The reconstructions display realistic dust plumes from
continental sources towards ocean basins following prevailing winds.
