The framework of PIANO. (IMAGE)

Science China Press

The framework of PIANO.

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(a). Given the PDE initial fields, PIANO first infers the physical invariant (PI) embedding via the PI encoder, then integrates it into the neural operator to obtain a personalized operator. After that, PIANO predicts the subsequent PDE fields with this personalized operator. (b). Training the PI encoder via self-supervised learning methods. (c). Integrate the PI representation with the dynamic convolution technique.

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