Fluid dynamics models are essential for describing a wide range of scientific phenomena and applications. Predicting solutions to fluid equations is often complex and computationally expensive due to their highly nonlinear and multiscale behavior, particularly in the presence of scarce or noisy measurements and incomplete model information. Recently, the development of PDE foundation models has led to improvements in predicting spatiotemporal systems under these settings. This talk will focus on advances in zero-shot and few-shot multimodal PDE foundational models for predicting solutions to incompressible and compressible flows. These approaches include operator-based methods, in-context learning, and autoregressive techniques.
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