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A New Formula for Pi Is Here. And It’s Pushing Scientific Boundaries.

New quantum mechanics research is introducing an advanced Pi formula, optimizing complex computations and reshaping ...
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PIANO: a new operator learning framework that deciphers and incorporates invariants from the PDE series via self-supervised learning and attention technique, achieving superior ...

(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 ...