  Scientific discovery and engineering design are currently limited by the time
and cost of physical experiments, selected mostly through trial-and-error and
intuition that require deep domain expertise. Numerical simulations present an
alternative to physical experiments but are usually infeasible for complex
real-world domains due to the computational requirements of existing numerical
methods. Artificial intelligence (AI) presents a potential paradigm shift by
developing fast data-driven surrogate models. In particular, an AI framework,
known as Neural Operators, presents a principled framework for learning
mappings between functions defined on continuous domains, e.g., spatiotemporal
processes and partial differential equations (PDE). They can extrapolate and
predict solutions at new locations unseen during training, i.e., perform
zero-shot super-resolution. Neural Operators can augment or even replace
existing simulators in many applications, such as computational fluid dynamics,
weather forecasting, and material modeling, while being 4-5 orders of magnitude
faster. Further, Neural Operators can be integrated with physics and other
domain constraints enforced at finer resolutions to obtain high-fidelity
solutions and good generalization. Since Neural Operators are differentiable,
they can directly optimize parameters for inverse design and other inverse
problems. We believe that Neural Operators present a transformative approach to
simulation and design, enabling rapid research and development.
