Explore the fourth stage of the machine learning process in this 23-minute video focusing on crafting loss functions for physics-informed machine learning. Dive into various case studies, including fluid velocity and Navier-Stokes equations, incompressible flows and Poisson equations, and Lagrangian Neural Networks with Euler-Lagrange equations. Learn about incorporating physics into loss functions through regularization terms and additional constraints. Discover the concept of sparse loss using the L1 norm and its application in SINDy (Sparse Identification of Nonlinear Dynamics) combined with autoencoders. Examine loss regularization techniques, parsimonious modeling, and equivariant loss functions. Gain insights into how these advanced concepts can enhance the performance and physical consistency of machine learning models in scientific applications.