Physics-Informed Neural Networks (PINNs) and Scientific Machine Learning
Talk, Ann Arbor Machine Learning Group, Ann Arbor, MI
Physics-Informed Neural Networks (PINNs) have transformed the numerical solution of partial differential equations (PDEs) by embedding them as soft constraints within the neural network training process. This approach has made PINNs a key component of the scientific machine learning (SciML) ecosystem. In this talk, we provide a broad overview of the PINN architecture, followed by three examples from physical systems: a damped oscillator with sinusoidal forcing, the Helmholtz equation, and a second-order elliptic eigenvalue problem known as the Gross-Pitaevskii equation. Furthermore, we demonstrate how PINNs can be used in practice and discuss key challenges, such as automatic weight selection via self-adaptive weight balancing, selecting the appropriate optimizer, and irregular boundary conditions. Notebook.