Digital twins are virtual models of physical systems that allow for more computationally cost-effective evaluation and optimization. Building digital twins often involves machine learning techniques that integrate data with underlying physical laws. In this seminar, I’ll explore two such techniques: Physics-Informed Neural Networks (PINNs) and operator learning. First, I’ll discuss the formulation of PINNs and how they can be utilized for solving forward and inverse problems. I’ll particularly highlight an application of PINNs for solving non-trivial parameter inference problems in viscoelastic fluids. Next, I’ll introduce operator learning which aim to learn mappings between function spaces. I’ll explore effective architecture choices for building powerful operator learning methods and present some applications and advantages of operator learning in solving partial differential equations.