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This paper introduces VSOPINN, a physics-informed neural network (PINN) framework that integrates differentiable soft Voronoi construction for sparse sensor data with centroidal Voronoi tessellation (CVT) to optimize sensor placement for flow field reconstruction. VSOPINN uses a shared encoder-multi-decoder architecture to handle multi-condition flow reconstruction and adaptively learns effective sensor layouts. Experiments on lid-driven cavity flow, vascular flow, and annular rotating flow demonstrate that VSOPINN significantly improves reconstruction accuracy, robustness to sensor failure, and clarifies the relationship between sensor placement and reconstruction precision.
Unlock better flow field reconstructions: VSOPINN adaptively optimizes sensor placement within a PINN framework, boosting accuracy and robustness even with sparse or failing sensors.
(short version abstract, full in article)High-fidelity flow field reconstruction is important in fluid dynamics, but it is challenged by sparse and spatiotemporally incomplete sensor measurements, as well as failures of pre-deployed measurement points that can invalidate pre-trained reconstruction models. Physics-informed neural networks (PINNs) alleviate dependence on large labeled datasets by incorporating governing physics, yet sensor placement optimization, a key factor in reconstruction accuracy and robustness, remains underexplored. In this study, we propose a PINN with Voronoi-enhanced Sensor Optimization (VSOPINN). VSOPINN enables differentiable soft Voronoi construction for sparse sensor data rasterization, end-to-end fusion of centroidal Voronoi tessellation (CVT) with PINNs for adaptive sensor placement, and unified layout optimization for multi-condition flow reconstruction through a shared encoder-multi-decoder architecture. We validate VSOPINN on three representative problems: lid-driven cavity flow, vascular flow, and annular rotating flow. Results show that VSOPINN significantly improves reconstruction accuracy across different Reynolds numbers, adaptively learns effective sensor layouts, and remains robust under partial sensor failure. The study clarifies the intrinsic relationship between sensor placement and reconstruction precision in PINN-based flow field reconstruction.
