  Reliable predictions of critical phenomena, such as weather, wildfires and
epidemics often rely on models described by Partial Differential Equations
(PDEs). However, simulations that capture the full range of spatio-temporal
scales described by such PDEs are often prohibitively expensive. Consequently,
coarse-grained simulations are usually deployed that adopt various heuristics
and empirical closure terms to account for the missing information. We propose
a novel and systematic approach for identifying closures in under-resolved PDEs
using grid-based Reinforcement Learning. This formulation incorporates
inductive bias and exploits locality by deploying a central policy represented
efficiently by a Fully Convolutional Network (FCN). We demonstrate the
capabilities and limitations of our framework through numerical solutions of
the advection equation and the Burgers' equation. Our results show accurate
predictions for in- and out-of-distribution test cases as well as a significant
speedup compared to resolving all scales.
