Figure from the paper.
The figures illustrate two types of deep learning-based partial differential equation (PDE) solvers. The left panel depicts the finite mapping using traditional deep learning methods, such as UNet and ResNet. The right panel showcases the infinite mapping achieved using a neural operator. Machine learning-based PDE solvers establish a mapping Gθ; from the initial condition A to the solution U (Gθ: A x θ → U). While both UNet and ResNet operate as PDE solvers by mapping between fixed finite spaces, they require retraining when the domain's resolution or shape changes. In contrast, neural operators are specifically designed to learn mathematical operators independent of discretization. By avoiding the need to directly learn a functional mapping tied to a specific discretization, these augmented solvers improve computational efficiency. Credit: Zhang et al. [2024], Figure 3
Editors’ Highlights are summaries of recent papers by AGU’s journal editors.
Source: Journal of Advances in Modeling Earth Systems

Accurately simulating and appropriately representing the aerosol-cloud-precipitation system poses significant challenges in weather and climate models. These challenges are particularly daunting due to knowledge gaps in crucial processes that occur at scales smaller than typical large-eddy simulation model grid sizes (e.g., 100 meters). Particle-resolved direct numerical simulation (PR-DNS) models offer a solution by resolving small-scale turbulent eddies and tracking individual particles. However, it requires extensive computational resources, limiting its use to small-domain simulations and limited number of physical processes.

Zhang et al. [2024] develop the PR-DNS surrogate models using the Fourier neural operator (FNO), which affords improved computational performance and accuracy. The new solver achieves a two orders of magnitude reduction in computational cost, especially for high-resolution simulations, and exhibits excellent generalization, allowing for different initial conditions and zero-shot super resolution without retraining. These findings highlight the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our ability to model the aerosol-cloud-precipitation system and develop digital twins for similarly high-resolution measurements.

Citation: Zhang, T., Li, L., López-Marrero, V., Lin, M., Liu, Y., Yang, F., et al. (2024). Emulator of PR-DNS: Accelerating dynamical fields with neural operators in particle-resolved direct numerical simulation. Journal of Advances in Modeling Earth Systems, 16, e2023MS003898. https://doi.org/10.1029/2023MS003898

—Jiwen Fan, Editor, JAMES

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