Self-adaptive loss balanced Physics-informed neural networks for the incompressible Navier-Stokes equations

Understand

There have been several efforts to Physics-informed neural networks (PINNs) in the solution of the incompressible Navier-Stokes fluid.

• The loss function in PINNs is a weighted sum of multiple terms, including the mismatch in the observed velocity and pressure data, the boundary and initial constraints, as well as the residuals of the Navier-Stokes equations.
• In this paper, we observe that the weighted combination of competitive multiple loss functions plays a significant role in training PINNs effectively.
• We establish Gaussian probabilistic models to define the loss terms, where the noise collection describes the weight parameter for each loss term.