A divide-and-conquer deep learning approach to reconstruct flow and temperature fields

Abstract

Reconstructing flow and temperature fields from limited sensor measurements is a critical capability for state evaluation, optimization, and control of flow and heat transfer processes. While deep learning has been harnessed for physical field reconstruction and has demonstrated impressive performance, it faces the challenge of achieving enhanced precision and computational efficiency, particularly when dealing with intricate, nonlinear problems. Inspired by the observation that numerous physical phenomena exhibit distinct behaviors within isolated regions of the spatial domain, such as boundary layers and separated flows, we introduce a novel deep learning approach that employs a “divide-and-conquer” strategy. In this methodology, the entire spatial domain is partitioned into various subdomains, each of which is entrusted to a dedicated neural network for precise reconstruction of the flow and temperature fields. Initially, the physical domain is segmented into discrete subdomains using K-means clustering based on cosine distance. Subsequently, individual deep neural networks are constructed to map from limited sensor measurements to the physical field within each subdomain. Finally, the separately reconstructed fields are amalgamated to constitute the ultimate physical field representation. To validate the efficacy of our approach, numerical experiments were conducted across four diverse cases: flow around a cylinder, turbulent channel flow, transonic flow, and conduction involving multiple heat sources. The results demonstrate the superior accuracy and efficiency of the proposed method. In comparison to the non-partitioned approach, our method achieves a minimum reduction of 44.6% in mean absolute error, simultaneously enhancing training efficiency by approximately 30.0% under the premise that the model can utilize multi-GPUs parallel training, all while maintaining a manageable model complexity.