Numerical Integration

This method applies Polya-Gamma latent variables as a way to obtain closed form expressions for full-conditionals of posterior distributions in sampling algorithms like MCMC.

MeshGraphNet is a framework for learning mesh-based simulations using graph neural networks. The model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. The model uses an Encode-Process-Decode architecture trained with one-step supervision, and can be applied iteratively to generate long trajectories at inference time. The encoder transforms the input mesh $M^{t}$ into a graph, adding extra world-space edges. The processor performs several rounds of message passing along mesh edges and world edges, updating all node and edge embeddings. The decoder extracts the acceleration for each node, which is used to update the mesh to produce $M^{t+1}$.