Physics-informed neural networks for solving partial differential equations - Prakhar Sharma (Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6)
In recent years, Physics-Informed Neural Networks (PINNs) have gained popularity, across differentengineering disciplines, as an alternative to conventional numerical techniques for solving partialdifferential equations (PDEs). PINNs are physics-based deep learning frameworks that seamlesslyintegrate the measurements and the PDE in a multitask loss function. In forward problems,these measurements are initial (IC) and boundary conditions (BCs), whereas in the inverse problemsthey are sparse measurements such as temperature recorded by thermocouples. The scope ofPDEs applicable in PINNs could include integer-order PDEs, integro-differential equations, fractionalPDEs or even stochastic PDEs. This chapter presents a brief state-of-the-art overview ofPINNs for solving PDEs. Our discussion primarily focuses on solution to parametric problems,approaches to tackle stiff-PDEs and problems involving complex geometries. The advantages anddisadvantages of several PINNs frameworks are also discussed.