Flow Field Reconstruction with Sensor Placement Policy Learning

Wei Wang (Beijing University of Post and Telecommunication) · Ruoyan Li (University of California, Los Angeles) · Guancheng Wan (University of California, Los Angeles) · Zijie Huang (Google Deepmind) · Zixiao Liu (University of California, Los Angeles) · Haixin Wang (UCLA Computer Science Department, University of California, Los Angeles) · Xiao Luo (UCLA) · Yizhou Sun (UCLA)

benchmark performance comprehensive experimentsdirectional transport-aware graph neural networkflow directionalityflow variabilityflow-field reconstructioninformation transportperformance disparity proximal policy optimizationreconstruction model performancesensor layoutssensor placement strategiessparse sensor measurementstwo-step constrained ppo

Flow‐field reconstruction from sparse sensor measurements remains a central challenge in modern fluid dynamics, as the need for high‐fidelity data often conflicts with practical limits on sensor deployment. Existing deep learning–based methods have demonstrated promising results, but they typically depend on simplifying assumptions such as two‐dimensional domains, predefined governing equations, synthetic datasets derived from idealized flow physics, and unconstrained sensor placement. In this work, we address these limitations by studying flow reconstruction under realistic conditions and introducing a \emph{directional transport‐aware Graph Neural Network (GNN)} that explicitly encodes both flow directionality and information transport. We further show that conventional sensor placement strategies frequently yield suboptimal configurations. To overcome this, we propose a novel \emph{Two‐Step Constrained PPO} procedure for Proximal Policy Optimization (PPO), which jointly optimizes sensor layouts by incorporating flow variability and accounts for reconstruction model's performance disparity with respect to sensor placement. We conduct comprehensive experiments under realistic assumptions to benchmark the performance of our reconstruction model and sensor placement policy. Together, they achieve significant improvements over existing methods.