Deep learning prediction method for aerodynamic forces on morphing aircraft considering physical monotonicity

Abstract Physical monotonicity is a pervasive phenomenon in the aerodynamic characteristics of aircraft, where the aerodynamic lift consistently increases with the angle of attack within the stalling range. Existing machine learning models for aerodynamic predictions often overlook this monotonicity, resulting in poor interpretability and credibility. To address this issue, we introduce a monotonic model, the Deep Lattice Network, which integrates the monotonicity constraint of the lift coefficient into machine learning based aerodynamic prediction framework. In this paper, we propose a novel deep learning model, Deep Lattice Cross Network, which aims to rapidly predict aerodynamic forces with high precision while ensuring monotonic constraints. Multi-Task Learning method is utilized to simultaneously predict both lift and drag coefficients, thereby enhancing the efficiency of the model. To optimize the training process and minimize costs, we adopt a unique two-phase deep network training strategy. Based on computational fluid dynamics simulation datasets of a morphing aircraft, the model is trained, and the efficacy of the model is tested by two interpolation and two extrapolation datasets. The results show a remarkable alignment with computational fluid dynamics outcomes across all test scenarios. Extended testing across a wider range of attack angles further highlights the superiority of the Deep Lattice Cross Network in upholding monotonicity. Incorporating monotonicity constraints not only improves predictive accuracy of the model but also greatly enhances its physical interpretability, which is crucial for advancing the development of more dependable aerodynamic prediction models.