论文标题
具有规律性结构的神经操作员用于建模由SPDES驱动的动力学
Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs
论文作者
论文摘要
随机部分微分方程（SPDE）是在包括大气科学和物理学在内的许多领域建模动态的重要工具。神经操作员，几代神经网络具有无限维空间之间学习图的能力，是解决参数PDE的强大工具。但是，他们缺乏建模SPDE的能力，而SPDE通常由于驾驶噪声而定期较差。由于规律性结构的理论在分析SPDE方面取得了巨大成功，并提供了概念模型的特征向量，使SPDES的解决方案良好，我们提出了具有规则性结构（NORS）的神经操作员，该神经操作员结合了用于建模由SPDES驱动的动力学的特征向量。我们对包括动态PHI41模型和2D随机Navier-Stokes方程在内的各种SPD进行了实验，结果表明NORS是分辨率不变的，有效的，并且在数量级较低的误差较低的情况下，具有适度的数据。
Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps between infinite-dimensional spaces, are strong tools for solving parametric PDEs. However, they lack the ability to modeling SPDEs which usually have poor regularity due to the driving noise. As the theory of regularity structure has achieved great successes in analyzing SPDEs and provides the concept model feature vectors that well-approximate SPDEs' solutions, we propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d stochastic Navier-Stokes equation, and the results demonstrate that the NORS is resolution-invariant, efficient, and achieves one order of magnitude lower error with a modest amount of data.
