Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity

Understand

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering.

• Such operator learning models not only predict particular instances of a physical or biological system in real-time but also forecast classes of solutions corresponding to a distribution of initial and boundary conditions or forcing terms.
• % DeepONet is the first neural operator model and has been tested extensively for a broad class of solutions, including Riemann problems.
• Transformers have not been used in that capacity, and specifically, they have not been tested for solutions of PDEs with low regularity.