Learned 1-D advection solver to accelerate air quality modeling

Abstract

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.Comment: Accepted as a workshop paper at the The Symbiosis of Deep Learning and Differential Equations (DLDE) - II in the 36th Conference on Neural Information Processing Systems (NeurIPS 2022