Enhancing complex Fourier characterization for temperature field reconstruction via multi-scale modulation and demodulation

The growing complexity of industrial systems necessitates precise thermal management through accurate physical field predictions. Deep neural network (DNN)-based reconstruction methods have become essential for this purpose, but often struggle to capture complex, fine-detail physical features due to uneven characterization across multi-scale spectral bands. These limitations can lead to unreliable system assessments and misguided decision-making. To address these issues, this paper proposes M-FNO, a novel temperature field reconstruction method that incorporates modulation and demodulation techniques within a spectral learning framework. MFNO's key innovation lies in its ability to perform cross-spectral characterization of multi-scale Fourier features, aggregating latent information from the full spectral range into a narrow low-frequency band to facilitate network training. The proposed method enhances the reconstruction of high-frequency thermal patterns while significantly improving computational efficiency. Validation through three case studies demonstrates that MFNO effectively improves the reconstruction accuracy, reduce GPU memory occupation, and expedites training speed. Moreover, it exhibits universal applicability, delivering robust performance across diverse physical field reconstruction tasks and mesh structures.