DeepOnet - Learning Nonlinear Operators Based on the Universal Approximation Theorem of Operators

This course aims to teach learners the concept of Deep Operator Networks (DeepONet) and how they can be used to learn nonlinear operators based on the universal approximation theorem of operators. The course covers topics such as the universal approximation theorem, designing DeepONet, learning explicit and implicit operators, and studying the effect of different formulations of the input function space on generalization error. By the end of the course, students will be able to understand and apply DeepONet to learn various operators, including integrals and fractional Laplacians, as well as deterministic and stochastic differential equations. The course utilizes a combination of theoretical explanations, examples, and demonstrations to cater to learners interested in neural networks, operators, and complex systems.