Self-adaptive loss balanced Physics-informed neural networks for the incompressible Navier-Stokes equations
arXiv:2104.06217 · doi:10.1016/j.neucom.2022.05.015
Abstract
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.
12pages,12 figures
References in corpus (3)
Cited by in corpus (25)
- A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
- Residual-based attention in physics-informed neural networks
- Physics-Informed Neural Nets for Control of Dynamical Systems
- Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains
- A practical PINN framework for multi-scale problems with multi-magnitude loss terms
- A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation
- Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks
- Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks
- Physical Activation Functions (PAFs): An Approach for More Efficient Induction of Physics into Physics-Informed Neural Networks (PINNs)
- GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks
- Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants
- Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells
- A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency
- Investigation of Compressor Cascade Flow Using Physics- Informed Neural Networks with Adaptive Learning Strategy
- Revisiting Tensor Basis Neural Networks for Reynolds stress modeling: application to plane channel and square duct flows
- A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systems
- Deep learning for full-field ultrasonic characterization
- Learning in PINNs: Phase transition, diffusion equilibrium, and generalization
- LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometry
- Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities
- Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
- Sequential learning based PINNs to overcome temporal domain complexities in unsteady flow past flapping wings
- Discontinuity-aware KAN-based physics-informed neural networks
- Bayesian Reasoning for Physics Informed Neural Networks
- Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables