ClimODE: Climate and Weather Forecasting with Physics-informed Neural
  ODEs
Yogesh Verma Markus Heinonen Vikas Garg
Climate and weather prediction traditionally relies on complex numerical
simulations of atmospheric physics. Deep learning approaches, such as
transformers, have recently challenged the simulation paradigm with complex
network forecasts. However, they often act as data-driven black-box models that
neglect the underlying physics and lack uncertainty quantification. We address
these limitations with ClimODE, a spatiotemporal continuous-time process that
implements a key principle of advection from statistical mechanics, namely,
weather changes due to a spatial movement of quantities over time. ClimODE
models precise weather evolution with value-conserving dynamics, learning
global weather transport as a neural flow, which also enables estimating the
uncertainty in predictions. Our approach outperforms existing data-driven
methods in global and regional forecasting with an order of magnitude smaller
parameterization, establishing a new state of the art.