DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation
This work improves the ability of PINNs to extrapolate solutions for complex physical processes, which is significant for scientists and engineers modeling dynamic systems.
The paper addresses the poor extrapolation performance of Physics-Informed Neural Networks (PINNs) for time-dependent nonlinear PDEs. They propose a novel training method that enables PINNs to accurately extrapolate solutions in time, achieving up to 72% smaller errors than existing methods in terms of the L2-norm.
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) [Raissi et al., J. Comput. Phys., 378:686--707, 2019] because the method parameterizes not only the solutions but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than existing methods in terms of the standard L2-norm metric.