Flow Reconstruction from Sparse Measurements with Upper and Lower Bound Constraints

Reconstructing the complete flow field from partial experimental observations is a fundamental task in fluid dynamics. Among existing flow reconstruction methods, Discrete Empirical Interpolation Method (DEIM) is notable for its computational efficiency and interpretability. However, DEIM may return unphysical values if the true state variable possesses upper or lower bound constraints. More specifically, DEIM estimates may contain values outside the physical bounds, such as negative mass density. In this talk, we present Constrained DEIM (C-DEIM), a method designed to accurately reconstruct flows with known upper and lower bounds. C-DEIM employs soft constraints to enforce these bounds, generating realistic reconstructions suitable for downstream tasks. We demonstrate the effectiveness of C-DEIM on two fluid flow examples: Rayleigh–Bénard convection and forecasting the spread of the 2023 Maui wildfires.