Flow Field Reconstruction via Voronoi-Enhanced Physics-Informed Neural Networks with End-to-End Sensor Placement Optimization

2026-03-10

AI Summary

High-fidelity flow field reconstruction is often hindered by sparse, spatiotemporally incomplete, or failed sensor measurements, and conventional methods struggle to balance accuracy and robustness. This work proposes VSOPINN, a novel framework that, for the first time, integrates centroidal Voronoi tessellation (CVT) with physics-informed neural networks (PINNs) in an end-to-end jointly optimized pipeline. By leveraging a differentiable soft Voronoi diagram and a shared encoder–multi-decoder architecture, VSOPINN unifies adaptive sensor placement and multi-scenario flow reconstruction within a single learning process. Experiments demonstrate that the method significantly improves reconstruction accuracy across various canonical flows, automatically generates highly efficient sensor configurations, and maintains strong robustness even when a subset of sensors fails.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

(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.

Problem

• flow field reconstruction
• sensor placement optimization
• physics-informed neural networks
• sparse measurements
• robustness

Innovation

• Physics-Informed Neural Networks
• Voronoi Tessellation
• Sensor Placement Optimization
• Flow Field Reconstruction
• Differentiable Rasterization