6 papers
ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics
Changhong Mou, Dinghua Xu, Xiyue Zuo +2
Modeling Hamiltonian systems over long temporal intervals remains a significant challenge due to intrinsic multiscale structures and rapid nonlinear transitions. While Hamiltonian…
PACE-FNO: Physics-Aligned Canonical Equivariance for Fourier Neural Operators
Jiaxiao Xu, Changhong Mou, Yeyu Zhang +1
Neural operators are often tested on states that differ physically from training data. A distinct failure occurs when the physical dynamics are unchanged but the observed coordinat…
PIP Net: Physics-informed Partition Penalty Deep Operator Network
Hongjin Mi, Huiqiang Lun, Changhong Mou +1
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal…
PAS-Net: Physics-informed Adaptive Scale Deep Operator Network
Changhong Mou, Yeyu Zhang, Xuewen Zhu +1
Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-i…
Lie Symmetry Net: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations
Xuelian Jiang, Tongtian Zhu, Yingxiang Xu +3
This paper employs a novel Lie symmetries-based framework to model the intrinsic symmetries within financial market. Specifically, we introduce Lie symmetry net (LSN), which charac…
Global Existence for the unstable Cahn-Hilliard equation in 2D with a Shear Flow
Bingyang Hu, Dinghua Xu, Yeyu Zhang
In this paper, we study the advective unstable Cahn--Hilliard equation on with shear flow: \begin{equation*} \begin{cases} u_t+Av_1(y) \partial_x u+\varepsilon Δ^2 u=…