  Climate models project an uncertainty range of possible warming scenarios
from 1.5 to 5 degree Celsius global temperature increase until 2100, according
to the CMIP6 model ensemble. Climate risk management and infrastructure
adaptation requires the accurate quantification of the uncertainties at the
local level. Ensembles of high-resolution climate models could accurately
quantify the uncertainties, but most physics-based climate models are
computationally too expensive to run as ensemble. Recent works in
physics-informed neural networks (PINNs) have combined deep learning and the
physical sciences to learn up to 15k faster copies of climate submodels.
However, the application of PINNs in climate modeling has so far been mostly
limited to deterministic models. We leverage a novel method that combines
polynomial chaos expansion (PCE), a classic technique for uncertainty
propagation, with PINNs. The PCE-PINNs learn a fast surrogate model that is
demonstrated for uncertainty propagation of known parameter uncertainties. We
showcase the effectiveness in ocean modeling by using the local
advection-diffusion equation.
