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Scientific discovery and engineering design are currently limited by the timeand cost of physical experiments, selected mostly through trial-and-error andintuition that require deep domain expertise. Numerical simulations present analternative to physical experiments but are usually infeasible for complexreal-world domains due to the computational requirements of existing numericalmethods. Artificial intelligence (AI) presents a potential paradigm shift bydeveloping fast data-driven surrogate models. In particular, an AI framework,known as Neural Operators, presents a principled framework for learningmappings between functions defined on continuous domains, e.g., spatiotemporalprocesses and partial differential equations (PDE). They can extrapolate andpredict solutions at new locations unseen during training, i.e., performzero-shot super-resolution. Neural Operators can augment or even replaceexisting simulators in many applications, such as computational fluid dynamics,weather forecasting, and material modeling, while being 4-5 orders of magnitudefaster. Further, Neural Operators can be integrated with physics and otherdomain constraints enforced at finer resolutions to obtain high-fidelitysolutions and good generalization. Since Neural Operators are differentiable,they can directly optimize parameters for inverse design and other inverseproblems. We believe that Neural Operators present a transformative approach tosimulation and design, enabling rapid research and development.

Neural Operators for Accelerating Scientific Simulations and Design