SBNO: Schr"odinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information
SBNO introduces an equation-free method that learns conditional operators for forward and inverse Partial Differential Equation (PDE) problems when data is missing. It uses diffusion Schrödinger bridge matching to learn time-dependent drift fields from paired data, enabling deterministic point reconstruction during inference without needing guidance weights or observation tuning. This offers a fast, scalable alternative for sparse observation tasks.