Researchers Propose Algorithm to Rebuild Fluid Flows from Limited Data

Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements presents key challenges owing to equation nonlinearity and restricted observation locations. Fluid velocity fields exemplify these situations. A new variational quantum algorithm is proposed for simultaneously reconstructing solutions throughout the complete spacetime domain. This differs from conventional techniques using temporal marching as it encodes the whole discrete spacetime solution into one variational quantum state, allowing combined optimisation of every time point. The related cost function incorporates both a discrepancy between sparse measurements and a physics-informed PDE violation term. Root-mean-square errors fell to approximately 10− consistently when reconstructing fluid velocities. Previously, achieving globally consistent solutions from such sparse data was unattainable due to computational limitations with traditional time-marching methods. The new variational quantum algorithm reconstructs these velocity fields by representing all…