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September 27, 2025Nature CommunicationsOpen Access

One-shot learning for solution operators of partial differential equations

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Machine learning method generalizes PDE solutions from single data input, indicating new approaches for complex systems.

One-shot learning enables solution prediction from a single partial differential equation instead of large datasets.
The local solution operator is defined and trained using a neural network for effective generalization across varied inputs.
Testing on multiple PDEs shows the method's effectiveness in complex geometries and practical applications.
This approach challenges traditional methods by reducing computational expense while preserving accuracy in solutions.

Jiao et al. (2025) studied this question.

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September 27, 2025Nature CommunicationsOpen Access

View Full Paper

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Authors

Machine learning method generalizes PDE solutions from single data input, indicating new approaches for complex systems.

One-shot learning enables solution prediction from a single partial differential equation instead of large datasets.
The local solution operator is defined and trained using a neural network for effective generalization across varied inputs.
Testing on multiple PDEs shows the method's effectiveness in complex geometries and practical applications.
This approach challenges traditional methods by reducing computational expense while preserving accuracy in solutions.

Jiao et al. (2025) studied this question.

View Full Paper

Ask AI

Bookmark