Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks
Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose Separation-Transfer Physics Informed Neural Networks (ST-PINNs) to address such problems. By sequentially resolving discontinuities from strong to weak and leveraging transfer learning during training, ST-PINNs significantly reduce the problem complexity and enhance solution accuracy. To the best of our knowledge, this is the first study to apply a PINNs-based approach to the two-dimensional unsteady planar shock refraction problem, offering new insights into the application of PINNs to complex shock-interface interactions. Numerical experiments demonstrate that ST-PINNs more accurately capture sharp discontinuities and substantially reduce solution errors in hydrodynamic problems involving multiple discontinuities.
Code (0)
등록된 구현이 없습니다.
Tasks
Transfer LearningSimilar Papers 제목 키워드 기반
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. W…
Operator learningDeep Euler method: solving ODEs by approximating the local truncation error of the Euler method
In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation …
Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula
Time-variant standard Sylvester-conjugate matrix equations are presented as early time-variant versions of the complex conjugate matrix equations. Current solving methods include Con-CZND1 and Con-CZND2 models, both of w…
Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp tra…
Physics-informed neural networks for solving forward and inverse problems in complex beam systems
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the …