Loss Balancing for Physics-Informed Neural Networks Considering Procedure for Solving Partial Differential Equations

With the development of machine learning, numerical analysis using neural networks has been devised. Remarkably, physics-informed neural networks (PINNs) enable physically consistent numerical analysis by introducing a loss function that conforms to relevant governing equations. Moreover, research is rapidly advancing for the application of PINNs to inverse analysis in areas such as physical property identification. For a PINN to learn governing equations, the weights of the loss functions should be properly determined because they have different roles in components such as boundary conditions, initial conditions, and governing equations. However, weight setting is generally challenging. We propose a loss balancing method considering the procedure for solving partial differential equations. The proposed method is validated through comparisons with conventional solvers.