Spatio-temporal dynamical systems, such as fluid flows or vibrating structures, are prevalent across various applications, from enhancing user comfort and reducing noise in HVAC systems to improving cooling efficiency in electronic devices. However, these systems are notoriously hard to optimize and control due to the infinite dimensionality and nonlinearity of their governing partial differential equations (PDEs), compounded by limited availability of training data. In this talk, I will present hybrid methods designed to overcome these challenges by blending data-driven, model-based, and physics-informed components. Specifically, I will discuss our recent efforts towards developing accurate surrogate models for fast prediction of PDE solutions as well as efficient strategies for learning feedback controllers for PDEs.

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