Neural operators for accelerating scientific simulations and design

Abstract

Scientific discovery and engineering design are currently limited by the time and cost of physical experiments. Numerical simulations are an alternative approach but are usually intractable for complex real-world problems. Artificial intelligence promises a solution through fast data-driven surrogate models. In particular, neural operators present a principled framework for learning mappings between functions defined on continuous domains, such as spatiotemporal processes and partial differential equations. Neural operators can extrapolate and predict solutions at new locations unseen during training. They can be integrated with physics and other domain constraints enforced at finer resolutions to obtain high-fidelity solutions and good generalization. Neural operators are differentiable, so they can directly optimize parameters for inverse design and other inverse problems. Neural operators can therefore augment, or even replace, existing numerical simulators in many applications, such as computational fluid dynamics, weather forecasting and material modelling, providing speedups of four to five orders of magnitude. Neural operators learn mappings between functions on continuous domains, such as spatiotemporal processes and partial differential equations, offering a fast, data-driven surrogate model solution for otherwise intractable numerical simulations of complex real-world problems.