AI-driven operator learning models like Fourier Neural Operator and DeepONet are redefining simulation speed, producing results in seconds instead of hours. Coupled with automation tools such as ...

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 ...

(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 ...