Abstract
<title>Abstract</title> <p>Deep learning provides an effective paradigm for solving nonlinear partial differential equations (PDEs) governing complex physicalfields, including thermal and acoustic fields. However, existing approaches often suffer from low solution accuracy in both fields, primarily due to inadequate feature extraction capabilities, which is further aggravated by inefficient multi-scale feature fusion mechanisms. To address these issues, this paper proposes FeatExtractNet, a point cloud-enhanced neural architecture with a focus on optimizing the feature extraction module. The framework adopts a domain-adaptive design: for irregular-geometry thermal fields, a PointNet-style architecture with multi-level feature extraction (MLFE) and cross-layer gated fusion (CGF) processes point cloud coordinates; for dense regular-grid acoustic fields, a Fourier feature residual MLP captures high-frequency wave structures while avoiding gradient attenuation from global pooling. Extensive validation experiments, including ablation studies and crossgeometry generalization tests, were conducted on 2D steady-state incompressible fluid-thermal coupling fields and acoustic fields under pure supervised learning. The results demonstrate that the framework achieves strong performance, with relative L2 errors of 0.0613 (u), 0.0605 (v) and 0.0543 for acoustic ptotal, representing 54.1%, 46.4%, and 65.3% reductions on these quantities compared with MPIPN, while pressure p and temperature T remain competitive.</p>