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Introduction
Neural Operators are a new class of deep learning models designed to learn mappings between infinite-dimensional function spaces. Unlike traditional neural networks that approximate finite-dimensional functions, neural operators can generalize across different input functions, making them powerful tools for solving partial differential equations (PDEs) and other scientific problems.
Why Neural Operators?
- Enable fast and accurate solutions to complex PDEs.
- Generalize well to unseen domains and boundary conditions.
- Reduce computational cost compared to classical numerical solvers.
Key Concepts
The most popular neural operator architecture is the Fourier Neural Operator (FNO), which leverages Fourier transforms to learn global representations. Other variants include DeepONet and Graph Neural Operators.
Applications
- Weather prediction
- Fluid dynamics
- Material science
- Biological systems modeling