A physics-informed coupled residual-Fourier neural network for multi-physics field prediction in laser manufacturing

In hybrid laser-MIG(Metal Inert Gas) welding, multi-physics field prediction in the melting pool is crucial for process optimization and quality control. However, the complex coupling among temperature, concentration, and velocity fields makes conventional simulations computationally expensive. This paper presents a Physics-Informed Coupled Residual-Fourier Network (PCRF-Net) method for multi-physics field prediction in the melting pool using simulation data and coupling physical residual equations. The method consists of a dual-branch architecture: the temperature and concentration fields branch uses deep residual networks, integrating energy conservation and solute transport equation residuals to predict temperature field and concentration distribution; the velocity field branch employs a Fourier-enhanced multilayer perceptron to predict velocity fields that capture long-range flow structures, while applying a temperature mask to restrict training to the molten regions. A stepwise training strategy is adopted, where the TC-Branch is trained first, and then the trained temperature field is used to guide the VF-Branch training, effectively reducing the complexity of multi-physics coupling. Compared to numerical simulation results, the method efficiently learns the temperature, concentration, and velocity fields generated by the coupling of laser and MIG heat sources, achieving second-level fast prediction. This demonstrates its great potential for real-time monitoring and parameter optimization in hybrid laser-MIG welding processes. • A novel stepwise training strategy is proposed that decouples the complex multi-physics coupling by sequentially training temperature-concentration fields and velocity fields, effectively solving the training instability problem that plagues traditional physics-informed neural networks when handling multiple coupled equations. • The method achieves approximately 5.73-fold speedup compared to traditional numerical simulations; after training, the model can predict arbitrary refined grids at second-level speed through interpolation methods without requiring re-simulation, demonstrating excellent grid resolution generalization capability.