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This review aims to clarify the architectures and applications of neural operators in solving parametric PDEs.

July 8, 2026MathematicsOpen Access

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

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This review analyzes neural operator architectures for PDEs in scientific computing, highlighting implementation and performance challenges.

This review aims to clarify the architectures and applications of neural operators in solving parametric PDEs.
Analyzed key neural operator models including DeepONet, PCANet, and Fourier Neural Operator.
Demonstrated architectures on canonical PDE problems like Poisson and hyperelasticity.
Discussed the use of neural operators as surrogate models within a Bayesian framework.
Evaluated neural operator performance on in-distribution and out-of-distribution samples.
Addressed challenges in prediction accuracy and generalization with new strategies.
Outlined directions for improving operator learning within scientific computing workflows.

Prashant K. Jha (2026) studied this question.

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This review analyzes neural operator architectures for PDEs in scientific computing, highlighting implementation and performance challenges.