用可微分的 Voronoi 构造,让神经网络自动优化传感器位置,提升流场重建精度。
Flow Field Reconstruction via Voronoi-Enhanced Physics-Informed Neural Networks with End-to-End Sensor Placement Optimization
- 通过可微分软 Voronoi 构造,将稀疏传感器数据转为网格化输入
- 在多个雷诺数下重建流场,误差降低且对传感器失效有鲁棒性
- 适合流体模拟、智能传感系统设计等需要自适应部署的场景
高保真流场重建在流体力学中至关重要,但受限于稀疏且时空不完整的传感器测量,以及预设测量点失效导致预训练模型失效的问题。物理信息神经网络(PINNs)通过融入控制方程减少对标注数据依赖,但传感器布局优化这一影响重建精度与鲁棒性的关键因素仍缺乏研究。本文提出一种带 Voronoi 增强的传感器优化神经网络(VSOPINN),实现稀疏传感器数据的可微分软 Voronoi 矩阵化,端到端融合重心 Voronoi 划分(CVT)与 PINNs 以自适应优化传感器位置,并通过共享编码器-多解码器架构统一优化多工况下的流场重建布局。在典型问题:驱动方腔流、血管流和环形旋转流上验证表明,VSOPINN 显著提升不同雷诺数下的重建精度,能自适应学习有效传感器布局,且在部分传感器失效时仍保持鲁棒性。研究揭示了基于 PINN 的流场重建中传感器布局与重建精度之间的内在关系。
原文摘要 · Abstract (English)
(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.
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