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

TL;DR

A PINN with Voronoi-enhanced Sensor Optimization (VSOPINN) is proposed that significantly improves reconstruction accuracy across different Reynolds numbers, adaptively learns effective sensor layouts, and remains robust under partial sensor failure.

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.

Figures (9)

• Figure 1: Diagram of the VSOPINN model. (a) Encoder/Decoder modules, (b) Attention-enhanced convolutional decoder. (c) Finite difference convolution kernel.
• Figure 2: Single-encoder/multi-decoder architecture of the multi-VSOPINN framework.
• Figure 3: Reconstructed velocity magnitude and pressure fields for the lid-driven cavity flow ($Re=100$). Compared with the CFD reference, the CVT-optimized sensor locations in VSOPINN yield more accurate resolutions of the primary vortex structures and corner singularities.
• Figure 4: Soft-Voronoi images of the velocity magnitude $|\mathbf{v}|$ for the lid-driven cavity flow ($Re=100$), constructed using the best-performing sensor subsets at different numbers of active sensors: $k=4$ ($\{S_1,S_2,S_3,S_4\}$), $k=3$ ($\{S_1,S_2,S_4\}$), $k=2$ ($\{S_2,S_4\}$), and $k=1$ ($\{S_4\}$), as highlighted in Table \ref{['tab:cavity_sensor_failure']}. The rasterization follows the differentiable soft assignment in Eq. \ref{['eq:soft_voronoi_weight']}, providing an image-like representation of sparse pointwise measurements on the reference grid.
• Figure 5: Flow field and absolute error distributions for the vascular flow ($Re=450$). VSOPINN exhibits superior accuracy over the baseline reference, particularly in capturing flow features near the bifurcation and unstructured wall boundaries.