Self-adaptive loss balanced Physics-informed neural networks
By Zixue Xiang, Wei Peng, Xu Liu, Wenjuan Yao. Neurocomputing, 2021
483 citations recorded by the source corpus.
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. We propose a self-adaptive loss function method, which automatically assigns the weights of losses by updating the noise parameters in each epoch based on the maximum likelihood estimation. Subsequently, we employ the self-adaptive loss balanced Physics-informed neural networks (lbPINNs) to solve the incompressible Navier-Stokes equations,\hspace{-1pt} including\hspace{-1pt} two-dimensional\hspace{-1pt} steady Kovasznay flow, two-dimensional unsteady cylinder wake, and three-dimensional unsteady Beltrami flow. Our results suggest that the accuracy of PINNs for effectively simulating complex incompressible flows is improved by adaptively appropriate weights in the loss terms. The outstanding adaptability of lbPINNs is not irrelevant to the initialization choice of noise parameters, which illustrates the robustness. The proposed method can also be employed in other problems where PINNs apply besides fluid problems.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ff9ce5fcf09aaaedfddef4038f31efed936e98e3
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In Statistical and Nonlinear Physics
Citations in the corpus
- A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks (2022, methodology): “In PINNs, the total loss is a weighted summation of multiple loss terms corresponding to the PDE and initial/boundary conditions, and different methods have been developed to automatically tune these weights and balance the losses [13, 14, 15].”