5 papers · 1 filter
Hypernetwork-Conditioned WENO5 Conservative-Form CNNs for One-Dimensional Conservation Laws
Yongsheng Chen, Wei Guo, Xinghui Zhong
We study a conservative data-driven discretization for one-dimensional hyperbolic conservation laws based on the classical fifth-order WENO finite-volume scheme and a hypernetwork…
Physics-informed machine learning for reconstruction of dynamical systems with invariant measure score matching
Yongsheng Chen, Suddhasattwa Das, Wei Guo +1
In this paper, we develop a novel mesh-free framework, termed physics-informed neural networks with invariant measure score matching (PINN-IMSM), for reconstructing dynamical syste…
Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks
Yongsheng Chen, Wei Guo, Qi Tang +1
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learnin…
Conservative semi-lagrangian finite difference scheme for transport simulations using graph neural networks
Yongsheng Chen, Wei Guo, Xinghui Zhong
Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely mul…
A multi-fidelity machine learning based semi-Lagrangian finite volume scheme for linear transport equations and the nonlinear Vlasov-Poisson system
Yongsheng Chen, Wei Guo, Xinghui Zhong
Machine-learning (ML) based discretization has been developed to simulate complex partial differential equations (PDEs) with tremendous success across various fields. These learned…