Joint optimization of sensor placement and sparse pressure field reconstruction with a two-stage framework for limited data

The pressure field on a high-speed train's surface is critical to aerodynamic design, underpinning the calculation of physical quantities, including lift, drag, lateral force, and overturning moment. However, due to space limitations and high experimental costs, only a limited number of pressure sensors can be installed on the train's surface, leading to sparse measurements and reduced accuracy. A common alternative is to use computational fluid dynamics (CFD) to generate simulated data for training machine learning models that identify optimal sensor locations and reconstruct full pressure fields from sparse measurements. While traditional methods like compressed sensing are widely used in prior work, neural-network-based methods remain underexplored, primarily due to the lack of suitable algorithms for sensor placement and the limited availability of CFD data. In this paper, we propose PROSNet (Pressure-field Reconstruction with Optimal Sensor placement), a neural network framework addressing both challenges. It includes a differentiable node selection module that learns optimal sensor placements and adopts a two-stage training strategy that encourages exploration of diverse sensor combinations, thereby learning a more generalizable representation of the pressure field. This strategy enhances the model's performance on unseen test data and mitigates overfitting. Quantitative results demonstrate that our model can accurately reconstruct the pressure field using only 2–8 sensors. Compared to the commonly used compressed sensing method, our approach largely reduces error on test data. These findings highlight the potential of neural networks as effective tools for recovering sparse pressure fields, offering clear advantages for the aerodynamic design of high-speed trains.