Nature

Neural operators for accelerating scientific simulations and design

The scientific method consists of a set of hypotheses formed through inductive reasoning based on observations, which are first systematically tested before being iteratively updated. However, testing ...
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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 ...
Nature

Temporal neural operator for modeling time-dependent physical phenomena

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator ...
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Learning neural operators on Riemannian manifolds

While artificial intelligence (AI) has made remarkable achievements in domains like image recognition and natural language processing, it encounters fundamental challenges when trying to deal with ...