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.

翻译：从稀疏传感器测量中重构流体流场是科学与工程领域的一项基础性挑战。测量点分布稀疏且流场具有复杂多尺度动力学特性，这使得精确恢复精细结构变得困难。此外，现有方法始终面临一个权衡：高精度模型通常计算成本高昂，而快速方法往往以牺牲保真度为代价。本研究提出BLISSNet模型，该模型在流场重构和基于松弛同化的数据同化任务中，在重构精度与计算效率之间实现了良好平衡。该模型采用类DeepONet架构，能够在任意尺寸的流场上进行零样本推理。在给定流场上完成首次模型调用后，部分网络组件可被预计算，从而显著降低后续在大尺度流场上进行推理的成本。因此，该模型的推理速度可超越径向基函数插值或双三次插值等经典插值方法。这种高精度、低成本和零样本泛化能力的结合，使得BLISSNet非常适用于大规模实时流场重构与数据同化任务。