BLISSNet: Deep Operator Learning for Fast and Accurate Flow Reconstruction from Sparse Sensor Measurements

Reconstructing fluid flows from sparse sensor measurements is a fundamental challenge in science and engineering. Widely separated measurements and complex, multiscale dynamics make accurate recovery of fine-scale structures difficult. In addition, existing methods face a persistent tradeoff: high-accuracy models are often computationally expensive, whereas faster approaches typically compromise fidelity. In this work, we introduce BLISSNet, a model that strikes a strong balance between reconstruction accuracy and computational efficiency for both flow reconstruction and nudging-based data assimilation. The model follows a DeepONet-like architecture, enabling zero-shot inference on domains of arbitrary size. After the first model call on a given domain, certain network components can be precomputed, leading to low inference cost for subsequent evaluations on large domains. Consequently, the model can achieve faster inference than classical interpolation methods such as radial basis function or bicubic interpolation. This combination of high accuracy, low cost, and zero-shot generalization makes BLISSNet well-suited for large-scale real-time flow reconstruction and data assimilation tasks.