Part 1: In the first part we will give an introduction to deep learning, emphasizing its applications in scientific computing through physics-informed neural networks (PINNs). Participants will first gain foundational knowledge in deep learning principles before exploring the structure and utility of PINNs, which integrate physical laws into neural network models to solve complex problems in fields like engineering and physics. The first part also examines current limitations of PINNs, such as computational challenges and accuracy constraints, alongside recent theoretical advancements that address these issues, equipping learners with both practical insights and critical analysis skills for using PINNs in real-world scenarios.

Part 2: The second part delves into advanced topics in physics-informed neural networks (PINNs) and their extensions, focusing on cutting-edge methodologies that address complex, data-driven problems in science and engineering. It is followed by an introduction to operator learning, a powerful approach for learning mappings between infinite-dimensional spaces. We will explore specific operator learning techniques, such as DeepONets and Fourier Neural Operators, which are particularly effective for solving problems governed by partial differential equations. Through practical examples, learners will gain a comprehensive understanding of these emerging methods and their applications in computational science and engineering.