Solution-Guided Machine Learning for Physical Field Prediction in Complex Geometries

Abstract The high computational expense associated with conventional numerical solvers and the limited generalizability of purely data-driven machine learning (ML) models present significant challenges for predicting physical fields in complex geometries. To address this limitation, we propose a solution-guided machine learning (SGML) framework that synergistically embeds a physics-informed analytical approximation within a convolutional neural network (CNN). This methodology extracts universal physical features from explicit solutions and generalizes them to arbitrary domains through a boundary distance function, thereby constructing a physics-guided approximate field. This approximation serves as a structured supplementary input to the network, substantially diminishing the learning complexity and enhancing extrapolative capability. Validation on irregular pipe flow demonstrates that the CNN-SGML framework exhibits superior data efficiency, robust generalization, and enables the use of more lightweight network architectures. In contrast to Physics-Informed Neural Networks (PINNs), the proposed approach exemplifies a synergistic coupling of data-driven learning and physical principles. Subsequent applications, including stress distribution in an elastic matrix with an Eshelby inclusion, stress concentration around an irregular cavity in a nonlinear material, and flow velocity and pressure fields surrounding an irregular obstacle, confirm the versatility of the method. Consequently, this framework establishes an efficient predictive tool for geometry-sensitive applications, such as fluidic device optimization and composite material design, particularly where high-fidelity simulation data is computationally prohibitive.