MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics.

Area of Science:

• Computational physics
• Machine learning
• Materials science

Background:

• Gradient-based meta-learning is typically used for image classification.
• Neural operators are emerging for learning complex physical systems from data, acting as surrogate models for PDEs.
• Material modeling faces challenges in data acquisition due to experimental costs and limitations.

Purpose of the Study:

• To develop a novel meta-learning approach for neural operators to enable knowledge transfer for solving partial differential equations (PDEs) with varying parameter fields.
• To improve sampling efficiency for learning solution operators of PDEs in material science.
• To create a universally applicable solution operator for multiple PDE-solving tasks.

Main Methods:

• Proposed a meta-learning framework for neural operators to transfer knowledge between governing PDEs with different parameter fields.
• Theoretically demonstrated that parameter fields can be captured in the first layer of neural operator models.
• Applied the approach to PDE-based datasets and a real-world material modeling problem.

Main Results:

• The proposed meta-learning approach enables effective transfer of solution operator knowledge across different parameter fields.
• Parameter field information is effectively encoded in the initial layers of the neural operator.
• The method successfully handles complex, nonlinear physical response learning tasks.

Conclusions:

• The novel meta-learning approach significantly enhances sampling efficiency for unseen material specimens.
• This method provides a provably universal solution operator for multiple PDE-solving tasks.
• The approach is effective for complex physical response learning in material modeling, addressing data acquisition challenges.