Kontolati Katiana, Goswami Somdatta, Em Karniadakis George, Shields Michael D
Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, ML, 21218, USA.
Division of Applied Mathematics, Brown University, Providence, RI, 2906, USA.
Nat Commun. 2024 Jun 14;15(1):5101. doi: 10.1038/s41467-024-49411-w.
Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.
由于计算成本高昂，使用传统数值模拟实时预测由偏微分方程控制的物理应用中的复杂动力学几乎是不可能的。神经算子通过近似无限维巴拿赫空间之间的映射提供了一种解决方案，但其性能会随着系统规模和复杂性而下降。我们提出了一种在潜在空间中学习神经算子的方法，便于对高维域上的高度非线性和多尺度系统进行实时预测。我们的方法在低维潜在空间上利用深度算子网络架构来有效地近似基础算子。在材料断裂、流体流动预测和气候建模方面的演示表明，与现有方法相比，具有更高的预测精度和计算效率。值得注意的是，我们的方法能够近似具有数百万自由度的大规模大气流动，增强天气和气候预测。在这里，我们表明所提出的方法能够进行实时预测，这有助于在科学和工程的广泛应用中进行决策。
