  We develop a wall model for large-eddy simulation (LES) that takes into
account various pressure-gradient effects using multi-agent reinforcement
learning (MARL). The model is trained using low-Reynolds-number flow over
periodic hills with agents distributed on the wall along the computational grid
points. The model utilizes a wall eddy-viscosity formulation as the boundary
condition, which is shown to provide better predictions of the mean velocity
field, rather than the typical wall-shear stress formulation. Each agent
receives states based on local instantaneous flow quantities at an off-wall
location, computes a reward based on the estimated wall-shear stress, and
provides an action to update the wall eddy viscosity at each time step. The
trained wall model is validated in wall-modeled LES (WMLES) of flow over
periodic hills at higher Reynolds numbers, and the results show the
effectiveness of the model on flow with pressure gradients. The analysis of the
trained model indicates that the model is capable of distinguishing between the
various pressure gradient regimes present in the flow.
