Scientific Machine Learning (SciML) is a fascinating new area where classic modeling methods based on partial differential equations (PDEs) are combined with machine learning’s approximation capabilities. It offers three primary subfields, which include PDE solvers, PDE discovery, and operator learning. Operator learning focuses on deriving properties from available data of a partial differential equation (PDE) or dynamic system.
In recent research, researchers from the University of Cambridge and Cornell University have provided a step-by-step mathematical guide to operator learning. The study has demonstrated that operator learning requires numerical PDE solvers to speed up the learning process and approximate PDE solutions. It also emphasizes the importance of carefully choosing problems, using suitable neural network topologies, effective numerical PDE solvers, stable training data management, and careful optimization techniques.
Operator learning is a promising field in SciML that can significantly help in benchmarking and scientific discovery. If you like the research, you can check out the paper for more information.