Physics-informed Neural Network Combined with Characteristic-Based Split for Solving Navier-Stokes Equations
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Abstract (arXiv)
In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and corresponding losses are separated, so the weights between output parameters are not considered. Not all partial derivatives participate in gradient backpropagation, and the remaining terms will be reused.Therefore, compared with traditional PINN, this method is a rapid version. Here, labeled data, physical constraints and network outputs are regarded as priori information, and the residuals of the N-S equations are regarded as posteriori information. So this method can deal with both data-driven and data-free problems. As a result, it can solve the special form of compressible N-S equations -- -Shallow-Water equations, and incompressible N-S equations. As boundary conditions are known, this method only needs the flow field information at a certain time to restore the past and future flow field information. We solve the progress of a solitary wave onto a shelving beach and the dispersion of the hot water in the flow, which show this method's potential in the marine engineering. We also use incompressible equations with exact solutions to prove this method's correctness and universality. We find that PINN needs more strict boundary conditions to solve the N-S equation, because it has no computational boundary compared with the finite element method.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 43 references that are in the map. First posted on arXiv 21 Apr 2023.
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References · 15
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- 2020Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domainscited by 79
- 2019Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equationscited by 67
- 2020Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacturecited by 48
- 2020DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretizationcited by 35
3 more
- 2021Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Datacited by 31
- 2020Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning methodcited by 29
- 2021Physics-informed Learning for Identification and State Reconstruction of Traffic Densitycited by 13
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