ALT Our latest research presents a framework that enhances deep #graphnetworks by optimizing message depth and filtering, effectively modeling long-range interactions while overcoming limitations like oversmoothing and underreaching. Learn how: https://neclab.eu/research-groups/system-platform-for-iot-and-ai/intelligent-software-system/publications#publications-2141. #NECLabs #ML

ALT Figure 12. Learning operators from stencils. From left to right, top to bottom: (a) On a Cartesian grid of data, CNNs may employ weight-sharing to fit finite-difference operators to data. (b) On unstructured data, similar weight-sharing may be achieved by lifting data first to a space of polynomial coefficients and learning how an operator acts on polynomials. (c) Learning operators as difference stencils allows learning of higher-order corrections. Shown here at a CFL condition of 10, a stencil learned from an analytic solution to the advection–diffusion problem does not exhibit the numerical dissipation of a traditional finite difference/volume discretization of the PDE. (d) Beyond learning physics, these frameworks can be used for supervised learning tasks on unstructured scientific data. Shown here, the drag force acting on a cylinder is regressed from nodal velocities on an unstructured finite volume mesh.