Adaptive Physics-Informed Learning for Downscaling Fluid Flows over Irregular Geometries

The computation of high-resolution flow fields, which is essential for various applications in engineering and climate sciences, is typically achieved by solving partial differential equations (PDEs). In applications such as design optimization or uncertainty quantification, solutions of these PDEs are computed for varying geometries. While physics-informed neural networks have emerged as a new surrogate, their usage for downscaling remains underexplored due to the need for repetitive and time-consuming training. In this work, we address this problem by combining an adaptive mesh learning strategy with a latent representation of irregular geometries. By adaptively refining the distribution of unsupervised training points during the training process, this strategy effectively captures critical couplings between physical fields over complex terrains. The performance is demonstrated through solving 2D stratified boundary layer-topography interaction for various Richardson numbers and mountain shapes. The numerical results show that the surrogate's downscaled fields reproduce local-to-global patterns such as trapped waves and upward propagating gravity waves. Moreover, it is shown that fine-scale fields can be predicted on new geometries using a single coarse field, such as buoyancy.