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Neural operators for accelerating scientific simulations and design


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.

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Fig. 1: Spectral overall analysis.
Fig. 2: Comparison of neural networks with neural operators.
Fig. 3: Diagram comparing a pseudospectral solver, a Fourier neural operator and the general neural operator architecture.

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A reference implementation for various neural operators including and examples on how to get started can be found at: Neural Operator Library,


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A.A. is supported by a Bren named professor chair at Caltech and AI 2050 senior fellowship by Schmidt Sciences. Z.L. is supported by an NVIDIA fellowship. M.L.-S. is supported by the Mellon Mays undergraduate fellowship. We thank B. Jenik for creating Fig. 2 and for general discussions.

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Azizzadenesheli, K., Kovachki, N., Li, Z. et al. Neural operators for accelerating scientific simulations and design. Nat Rev Phys 6, 320–328 (2024).

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