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Harnessing data to model complex physical systems has become a critical scientific problem in many science and engineering areas. The state-of-the-art advances of AI (in particular deep learning, thanks to its rich representations for learning complex nonlinear functions) have great potential to tackle this challenge, but in general (i) rely on a large amount of rich data to train a robust model, (ii) have generalization and extrapolation issues, and (iii) lack of interpretability and explainability, with little physical meaning. To bridge the knowledge gaps between AI and complex physical systems in the sparse/small data regime, this talk will introduce the integration of bottom-up (data-driven) and top-down (physics-based) processes through a Physics-informed/encoded Deep Learning paradigm for modeling, simulation and discovery of complex physical systems. This talk will show examples on data-driven modeling of nonlinear PDEs that govern the behavior of complex physical systems, e.g., wave propagation, reaction-diffusion processes, fluid flows, etc.

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