Physics-informed neural network for simulation of electromagnetic and temperature fields in electroslag remelting process

In the electroslag remelting (ESR) process, it mainly relies on thermal experiments or analysis via mechanistic models to realize the physical fields simulation of the electromagnetic field and temperature field coupled transfer, which has the limitations of high cost, a large amount of calculating data and high computing power requirements. A novel network based on physics-informed neural network (PINN) was designed to realize the fast and high-fidelity prediction of the distribution of electromagnetic field and temperature field in ESR process. The physical laws were combined with the deep learning network through PINN, and physical constraints were embedded to achieve effective solution of partial differential equations (PDEs). PINN was used to minimize the loss function consisting of data error, physical information error and boundary condition error. The physical laws and boundary condition constraints in the ESR process were considered to maintain high PDE solution accuracy under different spatial and temporal resolutions. Automatic differentiation (Autodiff) technique and gradient descent algorithm were used to optimize the network parameters. The experimental results show that compared with the mechanistic models, PINN can effectively replace thermal experiments to realize the physical field simulation of ESR process with only a few experimental data, which can avoid the disadvantages of pure data-driven network simulation that requires a large amount of training data. Moreover, the solution of PINN has good physical interpretability and reliability of simulation results. For simulating electromagnetic field and temperature field distribution, the training time of the network is only 140 and 203 s, and the regression indicators of root mean square error can reach 12.65 and 13.76, respectively.