Geometric-adaptive spatiotemporal deep learning framework for non-periodic unsteady flow prediction in deformable domains

Traditional experimental and numerical methods are inadequate for swiftly predicting the non-periodic unsteady flow field around deformation regions, particularly due to the complex coupling between time-varying geometries and transient flow physics. This paper presents a deep learning-based modeling framework that integrates adaptive mesh transformation techniques with a vision transformer-based time-fusion encoder–decoder architecture to address these challenges. The proposed approach establishes an effective spatiotemporal mapping between deformation geometries and their corresponding flow fields, overcoming key limitations of conventional methods in handling deformations while preserving critical flow features. Through comprehensive validation on continuously variable curvature airfoil cases, we demonstrate that our framework achieves remarkable prediction accuracy, with errors below 1.5% and correlation coefficients above 0.9998 on test cases. Notably, the framework demonstrates robust generalization performance, maintaining prediction errors below 3.5% even when extrapolating to flow conditions beyond the original training range. The study provides key insights into effective geometric parameters and loss function design for flow prediction in deformable domains. The implementation of the gradient-enhanced loss function has proven particularly effective, improving prediction accuracy by approximately an order of magnitude, while the additional incorporation of a structural similarity term further enhances the model's capability to handle complex input parameter configurations. By introducing a specialized neural architecture for deformation problems and an optimized processing methodology for deformation geometries, this work establishes an important reference for engineering applications of deep learning in unsteady flow prediction for morphing aircraft.