M34.3 CONNECT THE MECHANISM
Learn functions while using equations or families of solutions
You have two blood tests and a decay law. Put the law into the loss, check the residual by hand, and meet networks that learn whole families of solutions.
LESSON OVERVIEW14 min lesson
Lesson overview
You have two blood tests and a decay law. Put the law into the loss, check the residual by hand, and meet networks that learn whole families of solutions.
What you’ll explore
- Physics-informed models add equation and boundary residuals to learning, while neural operators map between function spaces; numerical accuracy, constraints, and extrapolation require independent checks.
GO TO THE SOURCE
Original explanations, connected to the research.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (Raissi, Perdikaris & Karniadakis, Journal of Computational Physics, 2019)Understanding and mitigating gradient pathologies in physics-informed neural networks (Wang, Teng & Perdikaris, 2021)Characterizing possible failure modes in physics-informed neural networks (Krishnapriyan et al., NeurIPS 2021)Can Physics-Informed Neural Networks beat the Finite Element Method? (Grossmann et al., 2023)Fourier Neural Operator for Parametric Partial Differential Equations (Li et al., 2020; ICLR 2021)Suggest a correction
A precise note can make an explanation better.
Choose the scene and describe what needs attention. Download a feedback file to share through a channel you already use. This page does not send feedback or connect you with a reviewer.