论文标题
部分可观测时空混沌系统的无模型预测
Learned 1-D advection solver to accelerate air quality modeling
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Accelerating the numerical integration of partial differential equations by learned surrogate model is a promising area of inquiry in the field of air pollution modeling. Most previous efforts in this field have been made on learned chemical operators though machine-learned fluid dynamics has been a more blooming area in machine learning community. Here we show the first trial on accelerating advection operator in the domain of air quality model using a realistic wind velocity dataset. We designed a convolutional neural network-based solver giving coefficients to integrate the advection equation. We generated a training dataset using a 2nd order Van Leer type scheme with the 10-day east-west components of wind data on 39$^{\circ}$N within North America. The trained model with coarse-graining showed good accuracy overall, but instability occurred in a few cases. Our approach achieved up to 12.5$\times$ acceleration. The learned schemes also showed fair results in generalization tests.
